Why should the government administer an airport terminal? It is ultimately a place for private businesses (airlines) to have reception and waiting rooms. I'd argue that the airlines should be buying their own land and building their own airports. Of course it makes sense (except maybe the busiest airports) for the different airlines to share a runway, and so it start to look like a public place. Airports are not public places though, and so I don't see why local governments should administer them (the FAA does have some safety operations at an airport).

While your typical playground makes sense for the city to administer, if the park is really a zoo it makes more sense for the city to not run it at all. However since the city benefits from the zoo it does make sense for the city to help the private zoo get started in a good location.