[bluesnowmonkey]

You only get locked out of a website if you delete your cookies while your email provider is down. How often does that happen?

This idea doesn't speed up the login process, but it accomplishes a few other useful things. The server doesn't store passwords, so a breach of the server doesn't compromise other services for which users had duplicate passwords. And users can't compromise their own accounts by choosing weak passwords. Both scenarios are commonplace.

[Fishkins]

To be fair, the user can still compromise all their accounts by choosing a weak password for their email account. It does reduce the onus on them from coming up with dozens of (hopefully) unique, strong passwords to one, which is certainly an improvement.

[jsmcallister]

Valid points, especially the security issues.