ZKP methods are just as draconian as they rely on locking down end user devices with remote attestation, which is why they're being pushed by Google ("Safety" net, WEI, etc).

The real answer to the problem is for websites/appstores to publish tags that are legally binding assertions of age appropriateness, and then browsers/systems can be configured to use those tags to only show appropriate content to their intended user.

This also gives parents the ability to additionally decide other types of websites are not suitable for their children, rather than trusting websites themselves to make that decision within the context of their regulatory capture. For example imagine a Facebook4Kidz website that vets posts as being age appropriate, but does nothing to alleviate the dopamine drip mechanics.

There has been a market failure here, so it wouldn't be unreasonable for legislation to dictate that large websites must implement these tags (over a certain number of users), and that popular mobile operating systems / browsers implement the parental controls functionality. But there would be no need to cover all websites and operating systems - untagged websites fail as unavailable in the kid-appropriate browsers, and parents would only give devices with parental controls enabled to their kids.