Libertarian anarchist theory is based on non-aggression, that is, the idea that capitalism can be a system where people deal only by consent. But the kind of consent it uses is "affirmative consent" - you said "yes", or you signed a contract agreeing ahead of time.
Feminism introduced me to the stricter idea of "enthusiastic consent" - you ongoingly and genuinely want to. From this improved perspective, contract is unacceptable (it's there to allow you to be forced despite no longer wanting to), and putting someone in an arm twisted position of "say yes or starve" is clearly not consensual. But this is precisely what capitalism does.
Honestly as things are now, I don't agree with the existence of money systems at all. I am not pro-tax, I'm against the whole of the money/paying/salary/finance system in its entirety. But tax is a weak hack to at least claw back a little economic equality. And breaking it without replacing it is harmful.
As to "we should be able to support roads" (or whatever), basically this has the same power and limitation as crowdfunding. A million ordinary people can scrape up a million dollars between them. But most of the economic power has already been sucked out of their reach - any individual in the 1% could pay that $1m out of their personal fortune and not even feel it. Spreading effort over the many when the few hold all the resources is a strategy doomed to fail.
Rothbard's position was that the only proper subject of an enforceable contract was the transfer of title to alienable property. Therefore, the only permissible use of force to compel specific performance would be to compel title transfer. A slavery contract, under this theory, is unenforceable because one's self and one's labor are not alienable.
This breaks down around edge cases relating to alienable property strictly necessary for life, though there's a case to be made that any property strictly necessary for life isn't alienable. That's a hole big enough to drive a system of socialized medicine through.
It is a very important right to be able to bind yourself via contract. In exactly the same way as is the _right_ of getting sued. Tom Schelling wrote about these issues in e.g. The Strategy of Conflict.
The right to commit yourself is important, because it will make other people more likely to commit themselves to you.
I can't even imagine how school would have worked for me that year I lived on my grandparent's farm without the whole school district having to pitch in.
As it stands what you've done is attacked the logic of the argument, as opposed to giving so much as a weak suggestion of how the problem would actually be solved.
Not all market transaction systems are effective at capturing sufficient amounts of consumer surplus to make provision of services possible.
As another example: many private (and public) transit systems were funded and financed by retail and real estate interests. By covering the fixed capital and much of the operating expenses of bus, trolley, and rail lines, they increased demand for their products and services. You see this today, but it comes in the form of providing "free parking" for retail establishments (you think those acres of parking outside your local mall or WalMart don't cost anything?).
Markets have failures too, my friend.