That really depends. A zero knowledge system would show to the verifier that the person is authorized for access _right now_, but thats just the answer to a particular challenge. Outside of the verifier who knows they came up with a random challenge without bias or influence, the response would mean nothing.

I think a lot of age verification systems are the solution to the real core of legislation - to make companies liable for underage viewing of content. To put such legislation in place without providing a feasible way to accomplish age verification would be argued as discriminatory.

In that sense, a zero knowledge system which doesn't give a company non-repudiation so that they can defend themselves in court may very well be insufficient. And that will require tracking identity long-term, although it could be done with a third-party auditor under break-the-glass situations with proper transparency.