You will. You have to pay for the roads with or without a tax. You're assuming people are too stupid to fix their own roads, and must pay a man to wear a badge and use their money to pay a private business to build the roads. Why not cut the middle man out and fund the roads voluntarily?
What a good little socialist.
its essentially game theory, there are no simple solutions.
to get the money for roads. For instance, it could be ad-supported. It could be a toll road. One could even imagine a system where the road company goes onto a site like kickstarter, and asks for the money. When enough has been gathered, the road is built/repaired/etc.