[grey-area]

Because your password database is a liability.

Arguably it's a greater liability for a business to be dependent on a third party for a connection with their users. It means they lose important user data like email (they have to ask for it usually), they're tied to that provider, and their website breaks for those users if that third party service goes down or is unreliable.

If you store your passwords securely you can't leak them, only a hash, but I agree it's a pain for users to manage multiple passwords/identities and can lead to too much password sharing.

Persona looks far more interesting than social login as it addresses the issue with who owns controls user data/logins and does not have a single point of failure, plus it provides the email.