A private road owner would be entitled to damages but there would have to be damages. If I paid you for a years worth of driving privileges, provided I don’t do X on your road, then I do X on your road, I would lose those privileges and you would still have the initial payment. As far as you’re concerned the contract has been fulfilled and you are whole. If my doing X resulted in damages then restitution could be sought. This would make something like speeding fines impossible to enforce. You could still collect those fines by incorporating them into a new contract or as a condition for reinstating the original.
I agree with you that privatization is the solution. I wanted to show where they are comparable, clearly you can’t enter into a contract in good faith when you are the one who settles the disputes. It can be very challenging to try to theorize how things, justifiably, should be. It’s downright depressing to try to theorize how to get there from here.