One issue that I see with this type of system is that it doesn't allow for parental/guardian oversight of what kids are doing or discussing.
Ever gone down the auto-suggestion rabbit hole on YouTube Kids? You start getting into weird and potentially disturbing territory much more quickly than you'd expect.
That's a good point. However, its possible to police YouTube Kids without destroying free speech. Policing the entire Internet and everyone else...not so much. That's the whole point of having the companies providing "kids" sites to register and have a specific set of regulations about the "kids" sites. Perhaps those regulations include parental controls.