Yeah, parent comment neglected the fact that drivers are paying via taxes and fees. Those may not be sufficient to pay for external costs, but that's how the roads are typically paid for.
You might be paying taxes and fees to license them but you could well have paid nothing to that city. I can drive through your city (unless you have tolls or entry passes, but the vast majority of cities don't have those). I can just use your streets for free.
There are federal, state and local taxes on transportation fuels. So sure, if you drive through the city without filling up your car there then you got a free ride on that city's roads, but not the state and interstate highways leading to it. But that's one of those things that averages out due to large numbers, and where it doesn't there is usually some rebalancing of revenues by government entities.
State routes? You probably are driving on a state route to/from that city. Also, cities can get funding from the state for road projects, so they do get access to this pool of money.