We need some kind of verification system that gives no extra information about users to the platforms, but I don't know if there's a true ZK way; it might require government involvement. I think that's fine. Govts could certainly run an age-verification system, give a signed yes or no token back to the user, with some permanently applied jitter per person so that platforms can't use cookies from returning users to figure out their birthday. As long as the government program has strict oversight to ensure it's not saving information about who's visiting what sites, it seems fine, or at least vastly better than entrusting photos of IDs to private 3rd parties.
"Meta, which owns Facebook, Instagram and Threads, began closing teen accounts from 4 December last year. It said anyone mistakenly kicked off could use government ID or provide a video selfie to prove their age."
So the bulk is done as you say but they still need* an age verification system for when they over-stepped.
* need here is because of the way the laws were written AFAIK.