If you think that privacy-preserving age verification is the most authoritarian way to tackle this problem, then you really, really don't understand authoritarianism.
Now if you have tons of better and practical solutions to tackle this problem, I would suggest you start writing about them. I haven't read a lot about those solutions (other than "just ask someone who is not me to do it"), what I hear is mostly people yelling that only bad parents and fascists disagree with them.