Por que a realocação do aeroporto não é feita gradualmente?

Moving airline by airline doesn't help that much:

• You still have the same chaos, just on a per-airline basis.
• The airports you mention are dominated by large carriers that have turned them into hubs (Turkish Airlines and Lufthansa). Even if you move all the other airlines one by one, you still have much of the pain of the big move when you move the largest airline.

And it has disadvantages:

• Connections: A large percentage of traffic through these hub airports are connecting passengers, and thanks to airline alliances and partnerships, many are connecting between flights from different airlines. Very few passengers (and even fewer high-paying business travelers) will willingly break their journey to go for a drive across a famously traffic-congested city to change airports. Customers will abandon your airport and fly other routes while this is going on.
• Equipment: When Denver International Airport moved, there was a massive overnight caravana "of more than 10,000 baggage carts, plane tugs, fire engines, catering trucks, de-icing machines and untold truckloads of tickets, tags and gift shop sundries" to the new airport. A similar operation occurred in Istanbul. If both airports must operate simultaneously, a fleet of equipment must be maintained at both airports during the overlap period. Much of this equipment is expensive, long-lasting, and will be difficult to sell or dispose of after the old airport is closed down.
• Staff: There's not an exact linear relationship of airport staffing to the number of flights. Many staff may work for contracted ground handling companies and serve flights from more than one airline. They can't be in two places at once.

This is still done to a limited extent though. Turkish Airlines operated a few flights out of New Istanbul Airport for several months prior to the big move, which allowed them to test systems and familiarize staff with the new airport. Some of these disadvantages can be mitigated by limiting the number of flights and choosing them strategically.

Gradual relocation essentially mean having to staff and equip nearly two full airports during the transition period. It is also annoying for the travelers that want to transfer planes and need to relocate to the other airport. They would then need to get transported to or from the new location and through security again unless a small short hop flight is established during the transition. In IST's case it's 35 km distance between the old and new location.

Having two busy airports close to each other is also a bigger challenge for air traffic control than a really busy one and a calm one.

The solution to the issues you mention can be solved by thorough preparation. Like making sure all the old badges work (or having the new ones passed out as they come in for their first day at the new location), make sure everyone knows where they need to report for work in the new location. Perhaps having some extra trouble shooters on hand to fix teething issues.

Gradually moving between airports is a living nightmare for connecting travelers.

Exactly that was done at Montreal Mirabel airport, a fabulous, spacious new replacement airport for Montreal Dorval (Trudeau). Montreal used to be Canada's main international hub. International flights were banned from the old airport, as incentive for airlines to move all operations to Mirabel. But they lacked the political strength to fully close the old airport, and never finished the high-speed-rail connection (or even highways) to Mirabel. Passengers needed to take an hourlong bus ride and re-clear security. This was so irksome that instead of consolidating at Mirabel, operators simply sent their international flights to Toronto instead, making it Canada's main hub.

They lost so many flights that Montreal didn't need two airports anymore, and they consolidated back at Trudeau. Mirabel's main terminal was scrapped and it's a race track now. A few cargo operations remain.

Then you have the case of Kai Tak, where they "threw the switch" properly, but due to teething pains, threw the cargo operações back to Kai Tak for a short while.

Em seguida, há Berlin.

My experience is when KUL moved from Subang (now SZB) to the new KL Intl Airport (KLIA).

The moving date was declared way in advance, I seem to remember the date was locked more than 6 months before, and a lot of airlines rescheduled their ops especially the nightstopping aircraft. Obviously Malaysia Airlines had to ferry a bunch of planes over but its a 10minute hop and done in the early hours so not much of an issue. Some of the ground equipment was ferried over earlier in the day (of the last day of Subang operations) but everything else was moved over once the last flight of the day was completed. I'm talking motorised stairs, K-loaders, belt-loaders, tractors, trolleys, dollies the works. It was quite a convoy of flat loaders. Stuff that could be driven on public roads were given temporary permits so you saw motorised steps and water/toilet trucks on the public highways!

The biggest change was moving from a host (MH) checkin environment to a homegrown common-use system which was integrated with the Baggage Handling System (BHS). The first days baggage handling was chaos with a lot of bags not making their flights.

A lot of items can't be duplicated not only in terms of equipment but also in manpower and its easier to make a clean cut and manage the problems for a 24hour period than drawing the pain over a period of weeks.