“Perfection not being an option” is one thing but as I demonstrated Rothbard’s principle offers no protection whatsoever for children against child abuse, which is hardly “a minor detail we can safely ignore.”
In my reply I also granted that current child protective laws and services are wretched. It’s not a refutation to repeat that. Until AnarchoLibertarians treat this with the significant attention it deserves (and as I said I give credit to Stephan Kinsella for at least thinking fairly deeply and candidly on it, though ultimately I thought his solution was unsatisfactory), their position is and should be unconvincing.
Which is the same with your #2: one might use that same #2 to argue that there should be no protective services or courts in an AnarchoCapitalist society whatsoever because “that is hardly the only way to solve a problem.” We do not do that with respect to other people (besides children), because we recognize that in a sufficient number of cases these “other way[s] to solve a problem” will prove insufficient, so protective agencies and courts are and ought to remain the ultimate recourse for redress.
This applies likewise to the “reputation is a sufficient guard against abuse” argument – most (though not all) parental child abuse takes place in private. But even when it doesn’t – child abuse is considered especially heinous in today’s society. Even today’s criminals look at child abusers with scorn. Child abusers are one of the few classes of criminals who are registered and their identities publicly recorded in a systematic way (something that would not happen in the version of an AnCap society you describe, since they would not be tried. I suppose people could create vigilante lists of suspected child abusers, with all the pitfalls that would have). Abuse continues.
I’m sorry, the handwave won’t do here; at least not with me. Especially since – and I wanted to be charitable, but some of the things Rothbard himself wrote on this, while frank, and followed as logical conclusions from his premises, was odious. I respect his candor (especially since he seems to have been a very decent man; I never met him, obviously, but he seems to have been), and so far those who have continued to develop his work have not found a good way to fix this consistent with the logic of his theory. We all know that in practice no theory will be implemented perfectly but when the theory contains a huge gaping hole (if anything, adults, who have greater resources and recourses than children, could better do without courts than children could), it’s proper to point out that the theory is fundamentally flawed and unimplementable as-is.
So, sorry; this is a case where it simply won’t do to contrast the existing situation with what one imagines it might be in an AnarchoCapitalist society, until AnCap theory itself can provide protection to children consistent with its own internal principles as strong as it provides to every other individual whose liberty it recognizes ought to be respected, with ultimate recourse to legal sanction if necessary.