I agree. I feel the flow of having browsers send some flag to sites is the most privacy-preserving approach to this whole topic. The system owner creates a “child” account that has the flag set by the OS and prevents the execution of unsanctioned software.
This puts the responsibility back on parents to do the bare minimum required in moderating their child’s activities.
If browsers are going to send flags, they should only send a flag if its a minor. Otherwise is another point of tracking data that can be used for fingerprinting.
What would be even more privacy preserving would be to mandate sites to send age appropriateness headers (mainstream porn sites already do this voluntarily).
Possibly it could be further mandated that the OS collect relevant rating information for each account and provide APIs with which browsers and other software could implement filtering.
And possibly it could be further mandated that web browsers adopt support for this filtering standard.
And if you want a really crazy idea you could pass a law mandating that parents configure parental controls on devices of children under (say) 12 and attach civil penalties for repeated failure to do so.
There's never any need for information about the user to be sent off to third parties, nor should we adopt schemes that will inevitably provide ammo for those advocating attested digital platforms.