Is there a plausible way they actually ban the use of VPNs? Like, they can make it illegal on paper, but even in China, which has long had strict restrictions on internet use, I've heard that VPN use is widespread.

It just all seems like performative whack-a-mole to me. The only people who can control what a kid sees online are their parents or guardians. A child is not buying themselves a laptop or an iPad.