Controlling VPN seems much easier, no? Since you have to pay for a VPN service, and I imagine most kids don't have a credit card to make arbitrary purchases independently, so it would have to bubble up to a parent.

The fact that you think you need to pay for a VPN service is a good illustration of the problem with this.

There's a plethora of free VPN services operating outside the reach of UK authorities.

My sons friend circle all figured out how to use free VPN's at around 8-9 to bypass bans on gaming servers.

That's assuming the child is smart enough to only use a paid-for VPN. I can foresee a lot of children being suckered into using a dodgy VPN.