Every power you grant the government is another knife they'll eventually stab you in the back with. Maybe you like your current government, but what about the next one, and the one after that?
Instead, just use the tools you already have access to. I was not opposed when California mandated that applications add parental controls, that's fine. If parents want to restrict their children's internet access, there's a continium there ranging from "prudent parenting" to "child abuse", but that can be worked out on a case-by-case basis. I am, however, rabidly against the state requiring you to dox yourself every time you log into a website, because inconceivably lazy parents can't figure out how to use the parental tools that they already have.
Expecting platform monopolists and dopamine dealers to design for this is folly. They are wired to try to normalize an unhealthy level of dependence on them. Their business model is addiction.
Okay but for your position to be tenable you have to then go to step 2, which is some parents are incompetent at doing this, and step 3, which is that, nevertheless, their children, who are randomized copies of them genetically, still somehow need and benefit from the filters that their parents can't or won't apply. Then you get to step 4, which is that all of the competent people must suffer so those children can get it from a heavy handed government solution. I don't see how you jointly accept all these steps; it means you want to have a tyranny of the incompetent over the competent. You must jointly assert that they are dumb while placing them up and over the not dumb. That's full on crab-bucket, dysgenics by force ideology.