If I were building the feature, I'd put the "adult" header behind a password.
But that's a solution only for the one browser. You'd need to forbid the OS account in use from installing new apps so the kid can't get a different browser. And now it's starting to be inconvenient for the parent.
The vast majority of kids would be stopped by the OS account restriction, especially now that they're growing up with iPhones instead of Commodore 64s.