What better model? Please explain.
A good model is laid out in Block's book on roads, and there are others who are exploring this area as well.
I guess one could opt of the tax code for the use of roads, but if it is later found he is using them, he has every right to be fined by the State, too.
You're assuming a "competing" model, in which some roads are public, some are private, "competing" for users. This is a poor model for your argument-because in a free society, people tend to prefer private roads for a number of reasons, including better upkeep and rule enforcement.
It's basically giving control of the roads over to private citizens who are able and willing to pay whatever price to own the roads for themselves. (That would be wealthy people like the Gates and Buffets of the world, not the average RPF anarchist, by the way.

) That's what I was getting at.
why is this less preferable than the wealthy and powerful government critters controlling the roads? (assuming that said millionaires would desire such a low-return investment-the returns would mostly be from advertising-we can assume that subscription costs for road use would decline over time, as with other products) A Gates or Buffet is not a government that can be easily bribed and manipulated, or simply pander to special interests as the government often does.