I think this is a big factor, and why I think this is a really bad UX. I've actually considered this method of authentication in the past, but the only thing this fixes is this site having to remember a password for you (and the accompanying side effect of the vulnerability of your password being compromised).

Now, the user not only has to hold onto the login email (or request a new one), but they have to access that email every time you use the site -- or, bookmark the URL (yuck). Not to mention the issue if they're on another device that doesn't have access to the email address.

This may work as a secondary, optional method of authentication. But having it as the only method isn't a good UX.