And sure, you can dispute if using evil to do good is evil all you want, but that debate is not a winning one for the “advocating evil” side, quotes around evil or not. Its why we have to go through so many lengths to obfuscate certain actions, and why folks, if you pitch them the same idea but sans obfuscation, will recoil in horror at the implication

The “evils,” under AnCap ideas of what counts as evil, of a typical modern state, have fairly broad public support.  So yeah, it actually can be a winning one, relative to some standards of evil.

I’m curious what categories you are specifically thinking of though, and actually potential solutions that cannot be achieved under anarcho-capitalist structures.

Population control, that will likely require some involuntary non-action that will have to be enforced, depending on conditions on the planet, once life-extension capabilities hit.  Under AnCap this is effectively impossible unless you cheat/exploit the AnCap rules by doing things like physically trapping people.

Actually caring for the poor at a sufficient rate.  Now I know you think this is unwinnable because “then the state becomes something to fight over too,” but just because a perfect solution has not yet been found does not mean that a good solution does not exist.  The AnCap answer is a non-answer and the actually-charitable will likely be outcompeted in the brutality of the market.

Environmentalism, since you have to resolve whether emitting carbon dioxide, or indeed any substance, violates the NAP, and if so what the appropriate level of response is, and people will necessarily disagree on this issue - they may even disagree on the facts without even just doing so out of being greedy.  (Edit: In fact, whether emitting carbon dioxide is a problem is defined by whether other people are emitting carbon dioxide, and if so, how much.)

Malthusian conditions are actually bad, and I won’t be persuaded into not even trying to prevent them because of AnCap principles I don’t even agree with.

Plus most of those random things Argumate keeps bringing up that bleed a little too much detail for your perfect axioms - which a well-designed Consequentialism can decide on IFF it actually matters to someone, but which your axioms cannot.