The state also sends a certain amount of fuel taxes to local governments in accordance with how many miles are travelled in an area.
New construction must privately pay to build the roads and then transfer ownership to the government. So the cost really is private. By far the most expensive part of maintaining roads is replacing bridges. Hence why so many bridges have rules about weight limits for trucks.
I suppose if you really wanted a user fee on roads you could have a system of tolls on bridges, intersections and interchanges, but that would be really unpopular.
If there is only one thing you take away from this discussion I hope it is:
Roadbuilding is fantastically, stupefyinlgy expensive. One can hardly believe just how expensive a safe, standards-based, high quality, durable stretch of asphalt is.
You know how you drive somewhere and then there are some cones set up and a lane of traffic is blocked off while two or three machines and a handful of guys repave a short section and then 20 seconds later the cones end and you're back up to full speed ? You just drove past millions of dollars of budget.