Age verification doesn't have to kill anonymity
Here's a bouncer standing outside a bar. He looks at your ID, sees you were born in 1994, hands it back, and lets you in. He doesn't photocopy it. He doesn't write your name in a ledger. He doesn't call your employer. Ten minutes later he's forgotten you exist.
That's age verification working properly. One question asked, one answer given, nothing kept.
Now imagine the same bouncer scans your ID into a database, stores a photo of your face, logs the time you arrived, and sells the whole file to a company you've never heard of. Same question. Wildly different consequences.
That second bouncer is what most of the internet is currently building.