Are you saying parents would choose not to block it, or children would get around it? Like you say people want to block it, but currently it's very hard while allowing access to Google and other resources, or it's easy to get around. Why does this require server verification?
For example, all devices could require your ZKP ID attestation to be usable unfiltered. Then the relevant apps/sites would be equally inaccessible to children. And then you remove the ZKP ID attestation because the device owner (parent, school, etc) already knows when the user is a child.