Or something similar. The important thing is that they shouldn't have to log in each time they visit the website, because then using email would cause the login

Or something similar. The important thing is that they shouldn't have to log in each time they visit the website, because then using email would cause the login process to be too slow. Again, using the password-less login for websites with sensitive data (such as banking) wouldn't work, since those sites require the user to log in for each session.