They would use force to prevent non-payers using their roads.
Really? You can think of no other way?
What other way do you suggest, ultimately?
You have built a valuable road.
People are using it against your will.
How do you stop them?
No we haven't. For almost 800 years, we have found that extracting money on threat of violence is the most efficient way to fund any endeavour of the ruling elites. That you would trade your freedom for some smooth tarmac and a shiny iPod says more about you than it does about alternatives to extracting money on threat of violence.
Every society ultimately ends up with someone with control of power running it, whether that power is the threat of force, or money or equivalent to be able to hire the threat of force, or agreements with other societies to be covered by the umbrella of their threat of force.
If it didn't, it would be taken over by the warlord next door, and would have no way of preventing it.
As long as the guy next door has a gang, and no morals, you need either a bigger gang, or to bring yourself within the protection of a someone else's bigger gang.
