Isn't that how parental controls already work?
There are problems, though:
1. The kids want to use Facebook. If parent A refuses to let their kid use Facebook, then kids B, C, D, E, F... all use Facebook and kid A becomes a social outcast. This actually happens. (Well, now it's other apps; kids don't use Facebook anymore.) This is similar to the mobile-phones-in-schools problem: if a parent doesn't let their kid bring a phone to school, and all the other parents do, that creates social isolation. When the school district bans the phones, it solves the problem for everyone. (So it's a collective action problem, really.)
2. Web browsers. Unless the parent is going to uninstall and disallow web browser use, the kid can still sign into whatever service they want using the web browser. I don't think parental controls block specific sites, and even if they do, there are ways around that, certainly.
I am very often the person who says that parents should actually parent their kids and not rely on the government to nanny them. But in this case I think there actually is value to the government making laws that make Facebook (etc.) less evil. And as a bonus, maybe they'll be forced to be less evil to adults too!