There is a subtle but important difference between blocking speech because children encountering it will supposedly be harmed, and blocking speech because the adults that encounter it will then be more likely to harm children.

A similar difference exists between preventing children from gambling, and preventing adults from gambling away the money required to feed their children.

Even though the harm in the latter examples is actually easier to substantiate, curtailing spreech because of the harm adults might do (even to children) is rather difficult, so demagogues tend to focus on the former for their bombast.