Don't get me wrong, I'm all for privacy. But between setting up the birthdate when creating my children's local account on their computers, and having to send a copy of their ID to every platform under the sun, I'd easily chose the former.
I'd even agree to a simple protocol (HTTP X-Over-18 / X-Over-21 headers?) to that.
Whilst parents absolutely should be guiding and helping the kids determine where they go online, and what they look at, I'm trying to envision where, or how, parents would be liable for them looking at something inappropriately "adult", barring actual child neglect.
A system like this would actually help parents be more confident that little Johnny wasn't going to stumble across something in appropriate, because, yes, in a way this is about control. It's about controlling what kids are exposed to before they are intellectually ready for it. Yes, there are potentially serious issues around that, such as limiting access to LGBTQ+ or other helpful material for young adults, but that should be a discussion around what information is needed at each age, rather than how to indicate that age.
Age gating on the open internet will happen, I don't see any way that it wont, what matters is how it is implemented. We know that submitting government issued ID to every site with potentially contentious content is a terrible idea; this neatly sidesteps the need for that, and actually forbids it.