Sure, planes are private property. The airport is not. Airports are government property. And when I'm, for example, going through TSA, I'm not doing so on a plane, but rather in the airport.

If you get your own plane, you won't have a problem finding a terminal without TSA.

Going through TSA is not a condition of using a government airport, it's just what happens if you use an airline.

In any case, being "government property" doesn't mean "completely free of regulation".

Municipal corporations ("cities") are not in all things the same as the government. Such as with property.