So who builds the roads now? The government? No. It just pays for them. It hires private companies to build them (in most cases. Sometimes they will have their own national road building company) So how is that working out for us? Is it the most efficient way available? Is it the most fair? I would doubt it. Just because the government has been the sole provider of something during your whole life doesn't mean it is impossible to provide in different (and better) ways. What about progress?
And who will build them in your ideal world? The same private companies. Then who will pay for them? Who gets to drive on them? If it's tolls, the poor with commutes to their jobs will be adversely affected by it, especially when taken in the context of minimum wage no longer being a thing. If it's everyone pays a flat fee, again the burden is on the poor because paying $1,000 out of $10,000 hurts a hell of a lot more than paying $1,000 out of $100,000 (similar arguments work for thing like police and fire departments, etc.) If it's everyone pays a percentage of what they make, that's straight up taxes and the government is whoever is collecting those taxes.
No matter how you slice it, your world will in all likelihood suck for the have-nots.