Mass of Earth's atmosphere dwarfs mass of aircraft
Earth's atmosphere has a total mass of about 5 x 10^18 kg. That so far dwarfs the mass of all aircraft - flying, parked, or long past their days of operation - that the impact on atmospheric pressure is well below anything that could ever be measured.
The big sky theory is alive and well! The only place that falls apart is when we have our aircraft tightly following common prescribed paths and heading to and from a limited number of terrestrial points. Unfortunately for airplane separation that is exactly what we do all day (and night) long every single day. I guess we can't do away with ATC.