I believe it is counter-productive, because "not having age verification" is a lost battle. Unlike E2EE (where it is impossible to give access "only to the good guys"), it is possible to implement age verification in a privacy-preserving manner. And look at the ChatControl fight: even though it is not possible, we are still struggling to convince politicians of it. Good luck with age verification where it is actually possible to do something.
It should be a public service: just like the government issues IDs already, it should run the privacy-preserving system that allows citizens to prove their age. We should fight for that, otherwise we will get non-privacy-preserving systems managed by private companies (which is already starting).