The content you do not want your child to interact with is your personal decision, and of course, varies from parent to parent. There is no permutation of acceptable administrative oversight to this issue I can imagine that would satisfy everyone reasonably, nor is there one that would not have chilling effects on free speech.

When it comes to content that is illegal specifically - that of course, should fall on tech companies to moderate. But that is the exception, in my view.

In short, your child's oversight is not one-size-fits-all - it is strictly your business, and perhaps your school's and childcare professionals'.