problem here is as follows:
how would you verify the age of someone without government id?
the answer very simple: you can't.
there is no (reliable) way to verify ID without government involvement, period.
"but it's the companies responsibility!"
well, how are they going to verify anyone's age?
that's right! by checking some form of government ID (passport, drivers license, etc.)
how would they know wether an ID is legit or not? by comparing to a government database.
so it's the government checking either way.
theoretically you could implement a hash-based system that's secure by comparing only hashed values against a government API without ever actually saving user information anywhere, similar to how "login with google/apple/facebook" and so forth work, but i doubt there's any government willing to spend the cash on such a system.
because that would actually work and could be made in privacy respecting way.
but because surveillance is the goal of any government trying to implement bullshit like this, it won't ever be done this way...
remember: it's always mass surveillance. never about "the kids", or "the crime", or whatever straw-man-of-the-week they pull out their ass at any given time.
requiring third party services is still problematic; i seriously do not trust any third party services to handle data as critical as ID.
having that leaked isn't like having your passwords or nudes leaked...it can seriously ruin entire lives!
I'd honestly rather have the government directly involved than some fuck-off "we're in it for the money", "how cheap can we go before we start leaking" company...
that said, i completely agree with the rest of what you said!
only i think that age restrictions is the wrong solution for the problem at hand, because it doesn't actually solve the problem.
the problem isn't (just) "kids have access to social media too early", the problem is "social media has become manipulative cesspool designed to brainwash entire populations"!
age verification doesn't solve issues like election interference, rising violence, privacy violations, misinformation, disinformation, etc, etc.
what does solve most, if not all, of those problems is properly regulating social media companies!
and it starts with forcing those companies to have open source, verified algorithms, to prevent them from being able to claim "they're committed to X", while blatantly ignoring any and all regulation.
the real problem is that just about nobody actually knows how exactly the massive social media platforms serve content, and how little control users have over their own algorithms.
solve that problem, and kids can be online just fine again! just like you and i were!
it is possible to return to a better internet, but that requires actually solving the root of the problem(s) at hand, instead of getting distracted with things like age verification, which, again, is just mass surveillance by a different name.