This is a good point, and a reason to do the right thing with regard to emails--which is to store a safe version of them (bcrypt).
Because while an email and a password is not public information, a username and a password isn't public information either. If you don't trust yourself to store the former, you shouldn't trust yourself to store the later much either.
Using bcrypt on email addresses is pants-on-head retarded. Please stop cargo-culting cryptography.
How do you propose to look up accounts by email address if they use a salted hash? You would have to bcrypt the email against every row in the database until you found the correct one. If you use a username to do the lookup instead, why store the email address at all? You can't use it for anything.
You're right and wrong. Right because it's a crazy idea.
Wrong, because it's the logical conclusion of the belief that emails must be treated with as much care as passwords. If you really think that, then you need to encrypt them, and therefore you have to give up the ability to look up user accounts by email address. All you could do is verify that a user-submitted email is associated with a user-submitted account. That's where you end up when you have that sort of paranoia about email addresses.
But that conclusion is, like you said, absurd, and I never should've implied otherwise. I wasn't thinking when I wrote it.
Particularly, the same kind of threat to other accounts belonging to the same person exists with username/password combinations as with email/password combinations; after all, people reuse username/password combos as much as email/password combos.
So, the same general class of people who you endanger by not storing email/password securely are endangered if you stop storying email and just have username/password.
And a lot of that class will have emails that can be quickly guessed by appending one of "outlook.com", "gmail.com" or some other popular free-webmail provider to the username, because if they reuse usernames and passwords, its quite likely they do it on their mail site and that they have a webmail provider. So while what Euler has done clearly has a significant convenience impact, it has negligible security impact.
Because while an email and a password is not public information, a username and a password isn't public information either. If you don't trust yourself to store the former, you shouldn't trust yourself to store the later much either.