anonymous question
You know, one could trivially answer that the state is unnecessary because — and then follows a long list of problems it causes. One could refer to the fact that the smaller the scale of state intervention, the more the economy flourishes. But values are subjective, and one cannot answer for everyone that the state is unnecessary. There are plenty of people who love having a boot in their backside right now, and many demand that it be shoved even deeper. Minarchy isn’t enough for them; they want socialism; they were taught in school that under socialism there is liberty, equality, and fraternity, or at least order and security.

Nevertheless, such an approach doesn’t work as an argument either. There is always a high percentage of conformists in society who will approve of the status quo, no matter how strange it is, so claiming that the majority sincerely and actively desires the state—to the point that they would come out to defend it—would also be rash.
Asking state representatives whether the state is necessary, and how about shifting a bit here to free up a small plot for ancap — well, that would be completely naive.
So, to get a correct answer to the question of whether the state is necessary, one must first achieve the appearance of a normally relatively pure ancap somewhere, and then let the market decide via migration and monetary flows. If people wishing “to make the state great again” consistently appear under ancap, then the state is necessary. For example, simply because one needs to have someone to grumble at. But if after a generation of living under ancap, the state is perceived as a strange, ancient, barbaric institution like trial by ordeal or some other omerta, then it means the state as such is not needed by humans; it’s just that it happens to exist now, and many put up with it.