If the kids are clever enough to have a second browser the parents don't know about, I'm pretty sure they'll find a way to bypass this. For example, who's stopping an older sibling giving remote desktop access to his browser?
It's the same as age limits on energy drinks, alcohol, tobacco etc. More of an inconvenience than a restriction if someone is determined enough.
We should focus on having parents teach their kids what they should and shouldn't be doing, instead of "blocking" them and pretending that solves the issue.