You can then prevent certificate forging by forwarding a cryptographic hash of the requester identity (generated by the website client), which will be included in the cert body so the website can verify the attestation was generated for this specific request, and it cannot be randomly reused.
Of course this doesn't solve the problem of using your grandma's id to bypass age restrictions, but I think that problem is worth the cost of privacy gains from corporations not validating IDs directly and screwing up like Discord's vendor did here.