I'm an ancap and I concede you make valid points here. The NAP is not viable as an absolute principle - it's too easy to come up with counter-examples that violate common sense morality.

But I've written a short article about how ancap philosopher Michael Huemer rehabilitates the NAP in his book The Problem of Political Authority.

Briefly, while the NAP is not valid as an absolute, aggression is usually wrong and thus we should consider an instance of aggression unjustified unless and until it is shown to be justified. Stealing a loaf of bread counts as aggression, but common sense tells us that your're justified in such if it it was the only way you could feed your family.

Still, there is a strong presumption that aggression is wrong, and we should assume state aggression is wrong unless and until it is shown to be justified.

Justification for aggression by private individuals is rare, but it turns out that it's even harder, much harder, to justify state aggression. So much so that those who incorrectly posited an absolute NAP overwhelmingly reached correct moral conclusions on state policies. The Problem of Political Authority explains why stat aggression is even harder to justify.

My article:
http://www.theproblemofpoliticalauthority.com/2015/08/huemer-and-the-nap/