Whoaaa assumptions!
Picking the airport and downtown are the only places on government property I occasionally park, and I pay per use for those. I rarely park on small roads because I have nothing to do there.
Roads can be private - owned by the person with the adjoining house. I live in a town in which the "roads" are private property with reciprocal easements to all other property owners in the town. It's awesome. There are no problems from people storing their RVs and trailers and junk on the street, because it gets towed for trespass. The town top budget item for our taxes is to hire companies to maintain what appear to be roads. This keeps the town answering to the people, because if they don't maintain the "roads" the people will reduce the taxes to about zero.
I'm serious, on what government property do I park for free?