You seem to have concluded that compulsion via the state is necessary. I don't know any ANCAPs that think a total lack of government would be utopia. But you have to compare the type of tyranny that exists via government compulsion against an ANCAP society. It is entirely unclear that ANCAP society would be more tyrannical.
And let me also point out that since ANCAPs aren't interested in forcing people to act in a particular way, the burden of proof doesn't lie with them. Instead, those seeking to apply force via government have the burden of definitively proving their system is superior. As of yet, you have not met that burden of proof.
See also Murray Rothbard on this topic:
"This point can be made more philosophically: it is illegitimate to compare the merits of anarchism and statism by starting with the present system as the implicit given and then critically examining only the anarchist alternative. What we must do is to begin at the
zero point and then critically examine both suggested
alternatives. Suppose, for example, that we were all suddenly
dropped down on the earth de novo and that we were all
then confronted with the question of what societal arrangements
to adopt. And suppose then that someone suggested: “We are all
bound to suffer from those of us who wish to aggress against their
fellow men. Let us then solve this problem of crime by handing
all of our weapons to the Jones family, over there, by giving
all of our ultimate power to settle disputes to that family. In
that way, with their monopoly of coercion and of ultimate decision
making, the Jones family will be able to protect each of us from
each other.” I submit that this proposal would get very short
shrift, except perhaps from the Jones family themselves. And yet
this is precisely the common argument for the existence of the
state. When we start from zero point, as in the case of the Jones
family, the question of “who will guard the guardians?” becomes
not simply an abiding lacuna in the theory of the state but an
overwhelming barrier to its existence."
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