The whole internet censorship doesn't make any sense to begin with. We already have decades of free online porn and everyone is fine. Why would we try to limit porn usage online now? It's a cry for regulations from overprotective nannies. These blocks don't work anyways as it just needs one single kid with access to porn and they'll share it with the others. To believe we can control that is crazy.

No tool in the world will block new sites emerging not yet added to the filter or people from installing an uncensored browser.

Not necessarily.

Recently we got a new LG TV that has an age lock option with some other family settings. The parent can turn it on with a PIN, and they can set up restrictions.
The same approach could be used here. But this would need 2 things: obviously support by the web browser app, and support by the OS to tie app installs, uninstalls and data wipes to the parent's code.

To help with cases when the device is sold, maybe the parent should press a button every year that they still want this, and also receive an email notification when the period is nearing it's end.

But a much better solution is that parents are dealing with their children.
They may see up some site filters, but when they notice that their child is using a workaround then it should be punished with taking away the phone.

Just an another HTTP header, flagging if user is an adult. Set it to False if OS reports that the account used has parental controls enabled.

This is just meant to keep children out, not protect state secrets.

Zero knowledge proof. Trusted issuer issues proof of birthdays. User submits proof of minimum age without disclosing additional information.