This would not work for really sensitive stuff (e.g. banking) where you need to log in each time you visit the site, but for normal sites it's really user-friendly.
My question is: Are the any disadvantages to this model? The only one I can think of is the situation where you've deleted your old email address and some time after that have to log in to a website that uses password-less login. But that is probably a rare occurance and could be fixed by contacting support.