If it's private and secure and isn't linked to your identity, we will share it and it will be useless because everyone who shares the same login is the same over-18 person.
If it is in any way linked to your identity, the data is online and a target for breach which will expose said identity.
There is no realistic way to implement this which both actually does anything at all, AND does not require adding attack surface for breaches.

Communities' flaws once hosted Reddit

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Please reread what I wrote. And regarding everything you use adding attack surface, that is the absolute best argument to not use an additional service such as the aforementioned 3rd party auth.
What are we doing here?

While that technically may not be a surveillance state, it would be an authoritarian state which could decide worker's rights or the history of slavery are "adult material" because what kid needs to know about them? Kids don't work or own slaves, so it's not suitable for them and they can't access it.

This idea sounds absolutely unhinged to me.