I don't know any libertarians or ancaps who insist that the non-aggression principle solves anything, much less everything. What we say is that it's simply the ethically Right Thing To Do, and that if "solving" a problem requires violating the NAF, then it's better left unsolved, even if there are negative consequences.
The idea that libertarians believe in some kind of "libertopia" is one of the most persistent, while completely unfounded and mistaken, myths that exists about libertarians. It's the libertarians who, more than any other group, take reality into account by acknowledging that we can't engineer a "perfect" society by using force against one another.
Libertarianism has pathologies at the edges? Big deal, so does every system that has ever been proposed as an alternative.