Indeed, I truly don't understand how simply enabling parental controls onto mobile devices handed to kids which then gets advertised to each website/app that they use isn't sufficient.

You make it an opt-in feature to "self-broadcast" that this device is being used by a minor. Solves 99% of the use cases. And for the remaining 1% — the really determined teenager — they'd never be stopped by this anyway. They'd social enginneer their way to access somehow.