That's what eBay does to me. You get to choose, at the time of login, between entering a password and getting an email verification, or just getting an email verification. At least with the bug report I had submitted to my bank, the password requirement had to be disabled from inside a settings menu, instead of being a clear option in the login prompt, but it that case it wasn't even a 2nd factor.

Long long ago the google toolbar queries could be reverse engineered to do an i feel lucky search on gmail. I created a login that (if @gmail.com) forwarded to the specific mail.

Unlikely to happen but it seems fun to extend email [clients] with uri's. It is just a document browser, who cares how they are delivered.

I hate this as well, especially since I have greylisting enabled on some email addresses, so by the time the email login is delivered, the login session has already timed out and of course the sender uses different mail servers everytime. So in some cases, it's nearly impossible to login and takes minutes...