Actually, the evidence brought in the trial in TOS episode "Court Martial" is CCTV footage from the bridge. It would appear that CCTV cameras exist or don't exist in needed locations as the plot demands. CCTV cameras have not become practical for the kind of use we put them to today until the 1990s (fonte), so it could be the writers haven't fully considered the implications of having such technology.

Aside from the already mentioned "Court Martial", there's assorted other episodes (including the films) where internal video recordings are used, demonstrating cameras are in routine use. It was one such in Jornada nas Estrelas III (which was, of course, just footage from the previous film) that allowed Sarek and Kirk to discover Spock had transferred his katra to McCoy.

The reason they don't show them being used routinely is Rule of Drama; it looks better on screen for one of the main characters to wander down to see what's happening, and by having someone on the bridge announce something "is on sensors" while staring at a console, they don't have to have video footage shown on a monitor while filming or added in post.

The Federation values individual liberty strongly enough to reject widespread surveillance

Real-world basis

In Jornada nas Estrelas (TOS, "the original series"), the Federation of the 23rd Century represents ideals held in the United States of the 1960s, while the Klingon Empire represents American opinions of the Soviet Union:

The Klingons took on the role of the Soviet Union in opposition to the United Federation of Planets playing the role of the United States.

— Westmore, Michael; Alan Sims; Bradley M. Look; William J. Birnes (2000). Star Trek: Aliens and Artifacts. Star Trek. p. 208. ISBN 0-671-04299-8.

One such American ideal is individual liberty:

"[Freedom] is a worship word. Yang worship."

— Cloud William; TOS: "The Omega Glory"

That episode makes it clear that Yangs represent Americans while Kohms (the Yangs' enemies) represent Asian communists.

The series characterized the Klingon Empire (the Soviet analogue) as a surveillance state:

"Do you know why we are so strong? Because we are a unit. Each of us is part of the greater whole, always under surveillance. Even a commander like myself, always under surveillance, Captain. If you will note."

— Kor, indicating a camera in his office; TOS: "Errand of Mercy"

Federation legal framework

Federation law resembles that of the United States on matters of individual liberty and privacy. For example, The Next Generation (TNG) mentions an analogue of the Quinta alteração:

PICARD: Oh, no. We cannot allow ourselves think that. The Seventh Guarantee is one of the most important rights granted by the Federation. We cannot take a fundamental principle of the Constitution and turn it against a citizen.

WORF: Sir, the Federation does have enemies. We must seek them out.

PICARD: Oh, yes. That's how it starts. But the road from legitimate suspicion to rampant paranoia is very much shorter than we think. Something is wrong here, Mister Worf. I don't like what we have become.

— TNG, "The Drumhead"

Federation social values

In Espaço Profundo Nove (DS9), three generations of the Sisko family discuss Earth's latest experience of martial law:

JOSEPH: The streets are going to seem emptier with them gone.

ODO: Would you be happier if they'd stayed?

JOSEPH: Oh, if they'd stayed, it wouldn't be Earth anymore, would it? It didn't seem right, all those phasers everywhere.

JAKE: Something wrong, Odo?

ODO: Am I the only one who's worried that there are still changelings here on Earth?

JOSEPH: Worried? I'm scared to death. But I'll be damned if I'm going to let them change the way I live my life.

SISKO: If the changelings want to destroy what we've built here, they're going to have to do it themselves. We will not do it for them.

— Joseph (Sisko), Odo, Jake (Sisko), and (Benjamin) Sisko; DS9: "Paradise Lost"

If the opinions of Joseph and Benjamin Sisko are typical, then individual liberty is still a strongly-held ideal among 24th Century humans

My impression is - although without hard evidence - that Starfleet uses a bespoke logging system for actions. With the communicators, it can be detected, where (and roughly, in what position) a crew member is. Voice recording and tracking console interactions does the rest.

From that log information, the visual representation is reconstructed (similar to the functionality of human memory). That makes it possible to view any situation from an arbitrary angle. Although the imaging is not able to tell the whole truth (fx, clothing variations would not be covered), but the visual interface allows humans to understand a situation much better than a textual log file.

That also explains, how - as seen in "Court Martial" - the log could be manipulated and viewed from different angles anyway.

"Court Martial" was filmed from 3 October 1966 to 11 October 1966. The story outline and the drafts of the teleplays were written from 3 May to 26 September 1966 with a few revisions up to 3 October. It was the 15th episode to be filmed.

We see the visual computer log of the bridge. The camera seems to be positioned high above the forward viewscreen:

UHURA: Meteorology reports ion storm upcoming, Captain.

KIRK: We'll need somebody in the pod for readings.

SPOCK: Mister Finney is top of duty roster, Captain.

KIRK: Post him.

SPOCK: Attention, Commander Finney, report to pod for reading on ion plates.

FINNEY [OC]: Message Received.

SPOCK: Officer posted, Captain.

(The ship suddenly judders)

KIRK: Stand by on alert status, Mister Spock.

SPOCK: Acknowledged.

HANSON: Approaching ion storm, sir.

KIRK: Warp factor one, Mister Hanson.

HANSON: Warp one, sir.

(There's another sharp jerk, and Kirk presses a button on his chair panel.)

[Courtroom]

SHAW: Reverse. Stop. Go forward with magnification on the panel. Freeze that. Captain Kirk is now signalling a Yellow Alert. Go forward, normal view.

When Shaw calls for magnification on the panel, it switches to an angle filmed from behind and above Kirk. When she says to go forward, normal view, the screen shows the whole bridge from a forward viewpoint, but not necessarily the same angle as previously.

[Bridge]

(On courtroom viewscreen.)

UHURA: Call from the pod, sir.

KIRK: Tie in.

FINNEY [OC]: Finney here, Captain. Ion readings in progress.

KIRK: Make it fast, Ben. I may have to go to Red Alert.

FINNEY [OC]: Affirmative.

KIRK: Hold our course, Mister Hanson.

HANSON: Aye, aye, sir. Natural vibrations, force two, Captain. Force three.

KIRK: Engineering, then ion pod.

UHURA: Aye, aye, sir.

CREWMAN [OC]: Engineering.

KIRK: One third more thrust.

CREWMAN [OC]: Working.

FINNEY [OC]: Ion pod.

KIRK: Stand by to get out of there, Ben.

FINNEY [OC]: Aye, aye, sir.

HANSON: Force five, sir.

KIRK: Steady as she goes, Mister Hanson.

(And the close up on the Captain's panel shows...)

And according to the transcript the computer log shows a close up from a different angle of Kirk pressing the jettison pod button prematurely, without a command from Shaw to specify the angle or the close up.

So the visual computer log seems to show the bridge from at least two different angles and with high resolution allowing for close ups when requested.

So if the computer logs of the Empreendimento were sent back in time to the 20th century they could have been edited into hour long episodes. That would make everything that we see and hear in Jornada nas Estrelas episodes accurate.

"The Menagerie, Part I" and "The Menagerie< Part II" were written from 12 August 1966 to 10 October 1966, with revisions up to 17 October. They were the 16th episode filmed, from 11 to 17 October 1966. Repeat, "The Menagerie" was filmed right after "Court Martial", so there was little time for the production staff to forget details of the plot of "Court Martial".

In his court martial, Spock shows images of events thirteen years ago on the Empreendimento and on Talos IV.

MENDEZ: Why? What does it accomplish to go there or to take Captain Pike there? I want to know why.

SPOCK: Are your comments a part of the record, sir?

MENDEZ: Yes, it's on the record.

SPOCK: Thank you. Request monitor screen be engaged.

MENDEZ: For what purpose?

SPOCK: To comply with the request you just made, sir, that I explain the importance of going to Talos Four.

KIRK: By asking why, you've opened the door to any evidence he may wish to present. Apparently what he had in mind.

MENDEZ: Present your evidence. Screen on.

SPOCK: This is thirteen years ago. The Enterprise and its commander, Captain Christopher Pike.

As I remember the screen shows the opening scene of "The Cage" with the camera zooming in on the bridge dome and passing thorugh it to show the bridge from overhead. When Spock speaks the camera angle shifts to a normal height from the overhead view, I think.

SPOCK [on screen]: Definitely something out there, Captain, headed this way.

KIRK: Screen off. Chris, was that really you on the screen? (flash) That's impossible. Mister Spock, no vessel makes record tapes in that detail, that perfect. What were we watching?

SPOCK: I cannot tell you at this time, sir.

MENDEZ: Captain Pike, were any record tapes of this nature made during your voyage? (flash, flash) The court is not obliged to view evidence without knowing its source.

SPOCK: Unless the court asks a prisoner why, Commodore. You did ask that question.

They resume watching the scene on the bridge. Then Pike goes to his quarters and Dr. Boyce visits him and they talk. It seems to me that would have been a good time for Kirk to say no ship makes record tapes that good, because respect for privacy would probably keep the computers from recording in a person's private quarters.

Or Kirk could have said that starships just recently started making record tapes in that detail, that perfect, instead of saying that they don't. He could have asked Pike if possibly there was an earlier experimental system to do so at the time of the Voyage to Talos IV, and his words suggest that he did, but Kirk failed to make it clear that ships do so now but just recently started, and changing a few words would have made that clear.

If

no vessel makes record tapes in that detail, that perfect

means that no recordings on the bridge are as detailed as seen in "The Cage", even though the bridge is the part of the ship likely to have the best automatic visual and sound recordings, then no scene in TOS can ever be an edited version of computer logs sent back in time to the 20th century.

At the best, written accounts of events on the Empreendimento could be sent back in time and used as the basis for scripts to film episodes using actors holding props and wearing costumes in sets. Then the characters would not really look or sound exactly like the actors, and the costumes, props, and sets could only approximate the look of the originals, if the information sent back in time to the 20th century even included visual details.

So "Court Martial" and "Menagerie" give greatly conflicting information about how detailed visual computer logs are, and thus of how faithfully TOS episodes reproduced the look and sound of the "actual" future events.

So how do we reconcile the two episodes?

One method would be finding the order of the two episodes.

The story outline for "Court Martial is dated 3 May and revised 26 June 1966. The first draft script for "Court Martial" is 15 July and the first draft for "Menagerie" is 12 August. The second draft for "Court Martial" is 6 September and for "Menagerie" is 3 October. Final draft for "Court Martial" is 26 September and 7 October for "Menagerie".

"Court Martial" was filmed from 3 October to 11 October and "Menagerie" was filmed from 11 October to 18 October.

So "Court Martial" has been made earlier than "Menagerie" all the way so far. But after filming came post production with optical and sound effects added and editing. I don't know when or in which order the episodes were completed and delivered to NBC.

The three most popular orders to view Jornada nas Estrelas episodes and/or to imagine that they happen in are:

1) production order, which puts "Court Martial" immediately before "Menagerie".

2) stardate order, in which "Court Martial" at stardate 2947.3 is followed by "Menagerie, Part I" at stardate 3012.4, with no intermediate episodes.

3) Broadcast or air date order, which puts "Menagerie" aired on 17 and 24 November 1966 ahead of "Court Martial" aired 2 February 1967, with seven episodes aired in between.

If "Court Martial" happens before "Menagerie" in both production and stardate orders, possibly enough time passed between the two episodes for Starfleet to stop making as detailed visual logs as it did in "Court Martial". Perhaps only a few starships and other Starfleet vessels were selected to experimentally make such detailed tapes, and many crew members complained about feeling watched or else acted unnaturally hoping to make good impressions on whoever watched the tapes in the future, and maybe Finney manipulating the tapes to frame Kirk was the last straw and Starfleet ordered all ships to stop making visual computer logs sometime before "Menagerie".

No momento da Jornada nas Estrelas II: A Ira de Khan Starfleet resumed making visual computer logs, at least in the engine room during emergencies, as seen in Star Trek III: The Search For Spock.

On the other hand, if "Menagerie" happened sometime before "Court Martial" as in their air date order, then perhaps Starfleet was inspired by the events in "Menagerie" to order the use of visual computer logs, and the Empreendimento might have started doing so a short time before "Court Martial".

Presumably that would have continued until the time of Jornada nas Estrelas II: A Ira de Khan como visto em Star Trek III: The Search For Spock.

And in either case the 90 or 100 years between TOS, TNG, DS9, and VOY gave plenty of time for the use of visual computer logs to possibly be started and discontinued and resumed a few times, so the practices in one era of Jornada nas Estrelas do not necessarily provide much evidence about the practices in other eras.