Alex, you're confusing free-riding with consumer surplus; they're different concepts.
You also seem to be confusing non-production of public goods with under-production; only the latter is what we (and every economics textbook) says will occur.
Also:
It would be untenable to deny that history provides many examples of situations in which there was no functioning monopoly on force-initiation over a significant region for a significant period of time, for any non-embarrassing standard of significance. I've never heard of a single case in the entire history of organized crime across hundreds of cities in scores of nations over multiple decades in which the unregulated market for protection behaved remotely like what is predicted by anarcholibertarian theory. This track record becomes even more dismal if you include all the cases in history in which there have been regions lacking effective sovereignty by a central authority. This amounts to an empirical falsification of the anarcholibertarian theory of protection markets that by the standards of social science is spectacularly conclusive.
Every single episode in which there wasn't a monopoly on force-initiation over a region becomes a test case for anarcholibertarianism. Despite the literally hundreds of such test cases, the only purported successes advanced for the theory involve a few thousand pre-industrial farmers sprinkled sparsely across medieval Iceland and the frontier of colonial Pennsylvania. In contrast to how even bastard forms of minarchism have been so spectacularly successful compared to all other significant social experiments, the track record of anarcholibertarianism is simply embarrassing.
