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Perhaps even hold parents culpable for not doing so, as a minimum supervision requirementEven the idea of prosecuting parents for allowing their child to access 'information,' no matter what that information is, just sounds like asking for 1984-style insanity.
A good rule of thumb when creating laws: imagine someone with opposite political views from yours applying said law at their discretion (because it will happen at some point!).
Another good question to ask yourself: is this really a severe enough problem that government needs to apply authoritarian control via its monopoly on violence to try to solve? Or is it just something I'm abstractly worried about because some pseudo-intellectuals are doing media tours to try to sell books by inciting moral panic?
As with every generation who is constantly worried about what "kids these days" are up to, it's highly highly likely the kids will be fine.
The worrying is a good instinct, but when it becomes an irrational media hysteria (the phase we're in for the millennial generation who've had kids and are becoming their parents), it creates perverse incentives and leads to dumb outcomes.
The truth is the young are more adaptable than the old. It's the adults we need to worry about.