Privacy

Honestly, that is how I would prefer it be done. But it isn't what OP asked for.

It would have to be set at an operating system level, with the OS providing an API for the browser to use, while the os itself restricts installation of unapproved apps (and to work, installation of apps would have to use an allow-list or a similar age-tagging system, where any app that includes general web access has to be 18+ unless it also implements age-gating correctly).

But yes, this would be the best system. Parental controls have never been very successful in the past, but I think part of the reason for this is that they've never been properly supported up and down the stack. The government should mandate that it is supported the whole way, so that parents really have the tools they need to enforce parental controls.

Edit: I thought this was a comment in another thread. My reply here only makes sense in that context.