Most online service providers who verify age are using third-party suppliers who don't provide any details of one's identity, just whether the user has been age verified or not. And much of that is done by recording a selfie, not handing over identity documents.
Stop trying to oversimplify the concept, it’s not a pub, it’s not a store, it’s a virtual service. This comparison doesn’t help us at all.
About the face and not ID: good thing we can’t identify someone using their face! /s