It’s absolutely possible to have privacy-preserving age verification, but it requires government to trust literally anyone, rather than just maintaining the validation themselves.

Go to gas station. Hand cashier your ID, like you do to buy liquor. Cashier gives you a one time use token/password to the age verification system website. You go there and upload a public key you generate before the OTP expires. Voila: now the site could easily verify that you control the private key and are thus of age, without having to know literally anything about you.

It only breaks if you treat everyone as a criminal until proven innocent, which is exactly what every government implementing this is doing, which is why it’s not really about porn at all but about removing privacy.