To start with, I'm not a huge fan of the idea that the Internet as whole could be legally obligated to assume I'm a child unless I provide every site I visit with a drivers license, for example.
But let's take your assumption to the next level: let's assume that there's some privacy-respecting way of doing this (I don't believe there is, but we'll temporarily pretend it exists).
I'm also not a huge fan of the idea that the Internet as a whole could be legally obligated to assume I'm a child based on criteria that are outside of my control. I personally think most of our experience with filters online have taught us that they're best implemented close to the consumer, not close to the source.
To be clear, both Youtube and the FTC are turning this into a dumpster fire. But the idea of filtering content that's designed for children is better than the idea of filtering consumers. It's just that this implementation of that idea is garbage and unnecessarily hurts creators.