Parents are massively on board.
And they are probably moving to a system where you need to link your device with a government issued cryptographic ID (i.e. passport) using zero knowledge proofs. With a system that ensures an identity can only be installed on one device at a time.
This means a parent would have to give up all social media accounts and chat apps on their own phone, in order to give their identity to their kids.
The parents could also check their kids phones and ground them if they find them using social networks.
The parents don't actually need their adult, childless neighbors to show their IDs to protect their kids, but it seems we're going down that exact path.