I think you’d want to also reverify now and then. People only rarely create accounts, which I think would make de-anonymizing someone from simultaneous breaches of site and verifier logs easier.

If you have to verify often enough, and age verification is required on enough sites that are widely used by the general public so that the mere fact that you are using sites that require age verification is not something you might need to hide, I think it would make it much harder to get useful information from log comparisons.