Age check happens by trusted entity (your government, not some sketchy big tech ass), they create a signed cert with a short lifespan to prevent your kid using the one you created yesterday and without the knowledge which service it is for.
Sorry, not sufficient.
Not secure.
" I certify that somebody is >18, but I don't say who - just somebody "
This is an open invitation to fraud. You are going to create at least a black market for these certificates, since they are anonymous but valid.
And I'm sure some real fraudsters have even stronger ideas than I have.