You can also use a password manager that’s not connected to a cloud. Or an encrypted usb stick. The problem with writing it on paper is, that people tend to use too short passwords or repeated passphrases. Using a really long master key and a key file with an encrypted database is safer than a cloud.
I can understand parents wanting some help from official sides. They are hated no matter what they do: Controlling internet access, especially of their teenagers? Helicopter parenting, or parents on a power trip. Letting their children use the internet? Neglecting assholes. Sitting next to their teenagers while they use the internet? Overbearing creeps smothering their children and possibly jobless leeches.
Parents have to at least be able to trust content filters.