Por que eles não pediram à C-3PO para abrir a porta do compactador de lixo?

Porque Luke não sabia o código da porta e não podia facilmente chegar até a porta para descobrir.

Brushing distastefully at the clinging slime, he made his way as rapidly as possible toward the hatchcover. Bending, he scraped accumulated detritus away, noting the number thus revealed.

“Open the pressure-maintenance hatch on unit 366-117891.”

_{^{Star Wars: A New Hope - Official Novelisation}}

Porque (no filme) ele depende de Han ler o número para ele, para que ele possa retransmiti-lo para o C-3PO, que pode retransmiti-lo para R2-D2.

Luke saw a hatch against the far wall. To C-3PO, he said, “Hey … hey, open the pressure maintenance hatch on unit number …” He turned to Han and asked, “Where are we?”
Han checked numbers that were etched on the hatch and read aloud, “Three-two-six-three-eight-two-seven.”
C-3PO made sure R2-D2 heard the numbers correctly, and the astromech opened the hatch.

_{^{Star Wars: A New Hope - Junior novelisation}}

O roteiro indica que Luke realmente não estava em condições de escapar, mesmo que a porta estivesse aberta.

INT. DEATH STAR - GARBAGE ROOM:
Meanwhile, Luke is lying on his side, trying to keep his head above the rising ooze. Luke's comlink begins to buzz and he rips it off his belt.

_{^{Star Wars: Final Draft Screenplay}}

Você precisa ter em mente que Luke tenta abrir a porta, e Han tenta explodi-lo, mas assim que eles entram, eles realmente não têm tempo para pedir à C-3P0 para abrir a porta porque episódio inteiro no espremedor é agitado.

^{deixei de fora qualquer diálogo para mantê-lo o mais conciso possível}

Han tumbles into a large room filled with garbage and muck. Luke is already stumbling around looking for an exit. He finds a small hatchway and struggles to get it open. It won't budge.

[...]

Han draws his laser pistol and fires at the hatch. The laserbolt ricochets wildly around the small metal room. Everyone dives for cover in the garbage as the bolt explodes almost on top of them. Leia climbs out of the garbage with a rather grim look on her face.

[...]

A loud, horrible, inhuman moan works its way up from the murky depths. Chewbacca lets out a terrified howl and begins to back away. Han and Luke stand fast with their laser pistols drawn.

[...]

Suddenly Luke is yanked under the garbage

[...]

Suddenly the walls of the garbage receptacle shudder and move in a couple of inches. Then everything is deathly quiet... With a rush of bubbles and muck Luke suddenly bobs to the surface.

[...]

Luke seems to be released by the thing.

[...]

Before anyone can say anything the walls begin to rumble and edge toward the Rebels.

[...]

Luke pulls out his comlink.
LUKE
Threepio! Come in Threepio!
Threepio! Where could he be?

INT. DEATH STAR - MAIN GANTRY - COMMAND OFFICE
A soft buzzer and the muted voice of Luke calling out for See-Threepio can be heard on Threepio's hand comlink, which is sitting on the deserted computer console. Artoo and Threepio are nowhere in sight.

A trooper pushes a button and the supply cabinet door slides open. See-Threepio and Artoo-Detoo are inside. Artoo follows his bronze companion out into the office. ...
The troops hustle off down the hallway, leaving a guard to watch over the command office.

[...]

THREEPIO
Use the comlink? Oh, my! I forgot I turned it off!
A New Hope - Script

Neste ponto, o compactador de lixo está quase fechado:

The walls are only feet apart... She's terrified and suddenly groans as she feels the first crushing pressure against her body.

Assim, a partir do roteiro, vemos que Luke nunca tem tempo, como mencionado por Valorum, também olhar para o número da unidade na escotilha, por causa do monstro e das paredes esmagadoras. E quando eles tentam entrar em contato com o 3P0, ele está se escondendo do Império, com o link de com-mail na mesa