There’s a whole network of radars and communication centers that are not part of any specific airport. How would you fund that through use fees at an airport?
On the other hand, if the fees corresponded to actual use, that would mean that the infrastructure along the most frequented corridors would automatically be the best funded one, which would probably be overall positive.
For VFR flights, communication with ATC is optional until/unless you get into busy Class D or better airspace.
If the fees are paid by any pilot passing through the ARTCC's zone, regardless of whether they use ATC, then it wouldn't be fair for the single engine piper putzing around over his backyard.
If the fees are paid by only pilots who use ATC, then pilots will stop voluntarily using ATC, leading to decreased overall safety.
In the US system, any revenue collection needs to be authorized by Congress. In fact, it is one of the arguments currently being argued in front of the Supreme Court about the tariffs.