Even speaking as an agorist, your faith in the market is a little extreme. It certainly has some useful and beneficial efficiencies to be sure, but believing that it will simply elevate the best and create a rising tide that will raise all standards is a little naive I think with regards to what we see in the world where markets reign.

Assuming humans are perfectly rational agents with equal information it works, but that's not how humans really are. Humans are dumb, panicky, emotional animals, and the difference between the most incompetent of them and say cows are not as wide as our politically correct institutions would like to force us to believe.

You would do well, even in an ancap society, to voluntarily donate to charities that pursued socially beneficial objectives so that you reaped the benefits of their actions. This is pretty much the ancap response to tragedy of the commons. Vaccination and libraries are not a bad example of where this makes sense imho. There's nothing strictly contrary to ancap doctrine to point out that choosing not to clean your proverbial home will result in you living in a mess, so you might want to do that occasionally.

It is not enough to point out that simply because states provably fail, markets are perfectly efficient.