Some third party is going to have to verify that that's true. Which means some third party is going to have to have access to my private data, to verify that my public key belongs to a person whose private data meets whatever requirements are being asked about. That third party will end up being a big tech company.
Your example about CAs is not relevant because CAs only need to verify that someone has control of a particular web endpoint. They don't need to verify the private information of whoever that person is. So the information they need is much less intrusive than the information a third party who is going to attest that public keys belong to people meeting things like age requirements would need to have. Yes, once a third party has attested to your age certificate, they aren't involved with how you use it--but that third party has to have a lot more private information about you to be able to make that attestation, than CAs currently have about website operators.