You're right. My objection is that in practice there'd be no way to avoid violent chaos. Abortion is one of the things that will lead to it (or else go unpunished altogether).
Annalex-Hoppe Theorem. In a multiple law enforcer environment, independent judiciary will reflect the community standard of justice.
In the case of abortion (and, no doubt, other issues) there is no community standard. You'd have to have such a standard formed and the exclusion of "wildcards" already in place before you can hope to have a decently functioning anarchist society, and I just don't see that happening. And if it does happen, it could be undone by any number of factors.
With respect to issues where there is no community standard, how is the anarchist situation different from what we have now with a single law enforcer?
I can tell you how it is worse. Now a single law enforcer, the state, is combined with hierarchical judiciary. Thus we have our Supreme Court Commissars ensuring a sclerosis of the community. In fact, we barely know what the community standard is on abortion. The pro-abortion folks tell us that the point is not worth arguing because the Supreme Court already decided the issue. The pro-life folks point out that while there is no consensus on banning abortion, there is a consensus on banning partial birth abortions, parental notification and welfare abortions, and each time the court is to the left of the consensus. I'd much rather have chaos (another word for which is local control).