I don't think hashes of email addresses are very secure. You can get all of the email addresses from the smtp logs. There are also massive email lists out there that the attacker could run the hashes against, like the adobe leak. Email addresses typically follow specific formats, such as firstname.lastname@gmail.com, and would be quite easy to bruteforce/dictionary attack. If the hashes were to ever leak, easily >95% would be cracked, especially if they are using single-round SHA512.
I feel like particularly if you are storing user data in a way that is visible to others, you have a responsibility to be able to contact the author of the data, given potential abuse?
1) you can hash together email + randomsalt + password and then store randomsalt and the hashed value<p>2) you avoid passwords altogether by giving a user an authentication token to be saved as a bookmark perhaps? The token contains a cryptographic signature