Air traffic controllers function similar to toll booth operators. You need to pay them when you get on and pay them when you get off (depending on the structure of the turnpike). Air traffic controllers seem to provide similar services. They provide safe access to and from the sky. In the same fashion that those who use the toll road pay for access, why shouldn't airlines pay for access to the skies?
I have no doubt that the airlines would simply pass this charge along to the traveler, but if the traveler is benefiting from the work of the air traffic controller, why shouldn't they pay for it?