You don't tell your child not to go out in public, you teach them how to go out safely.

I think this particular argument actually illustrates what I think is the more serious problem with such laws: not that the government can't regulate what children are allowed to do in school, but that the regulation paints with too large a brush. The thing about your analogy is that it's true only past a certain age. Below a certain age, I would most certainly tell my child (assuming I have one some day) not to go out in public. Above a certain age, such a blanket rule is no longer appropriate.

The solution as I see it is to let local school districts craft acceptable use policies, and enforce them, with age-appropriate terms for the different school levels. I remember doing this in my high school ten years ago and it worked reasonably well. The policies would be publicly posted and parents could raise concerns via the school board if needed.