One thing I said before is the question of what is the research on this, and how do we know child internet safety is actually a problem? I don't know the statistics on this, and I haven't done much studying on it yet. So I will admit that I have been operating under the premise that this is an issue to begin with. Someone mentioned routers with parental blocks. Aside from being able to easily disconnect from the network (inevitability for kids because it's easy and they have plausible deniability, in my opinion), if child internet safety is currently an issue, then clearly there is something about it that isn't working.
But even if it happened purely at the OS level, it would be laughably unenforceable at best.
Don't get me wrong, it would still require another component whether that be a requirement for websites to query the OS via the browser, or a database of "bad" websites.
Now, if you want there to be an app that handles this, that's your opinion and I respect that. Personally, I would rather it be built into the OS. Least of all because already-on-your-device is easier than something parents need to research and download on their kids' devices. More significantly, if this kind of capability becomes an expectation for your general usage OSes to have, then that's less incentive for some company to come in and try to capitalize off of it and charge $12.99 per month, and then still have incentive to collect and sell data on which sites are being visited. I mean, you can be reasonably sure that Microsoft is gonna do that too, but that would be another reason to switch to a Linux distro that doesn't do that.