It's not just age verification: the identity-verifying document's image is kept on servers for future use. Theoretically by governments verifying, practically so that everyone's identity can be highjacked in a leak.

Adult verification is simply determining a single bit: is this person an adult or not? We have had zero-knowledge proof for ages: if the government really wanted to determine this single bit, it could do so without jeopardizing everyone's privacy and online security.