what prevents you from leaking your token on the internet, so everyone can use it? it has to be revokable somehow. to be revokable it has to be correlatable, so you can tell where the same token is used across multiple sites. which leads to easy deanonymization.
ZKP is window-dressing. it's still a major privacy intrusion. don't fall for it.
(also, it paves the way for lgbt issues, sex ed, harm reduction and activism to be censored behind the 18+ barrier, but that's a different matter.)