How do you send a password reset email with this. Eventually your mail server will need the plaintext address in order to send the email. And that point can be leaked in a data breach.
It's idealistic to think this could solve data braches because businesses knowing who their customers are is such a fundamental concept.
I don't think this is possible with FHE alone.
A password reset e-mail is supposed to expire pretty quickly though, so would it really matter in practice?