I've got a little generic login tool that bits I write myself use for login, using this method, but it is not for anything sensitive or otherwise important (I just want to identify the user, myself or a friend, so correct preferences and other saved information can be applied to the right person, and the information is not easily scraped) - I call it ICGAFAS, the “I Couldn't Give A Factor” Auth System to make it obvious how properly secure it isn't trying to be!
Another issue that email based “authentication” like this (though one for the site/app admins more than the end user) has is the standard set of deliverability issues inherent with modern handling of SMTP mail. You end up having to use a 3rd party relay service to reduce the amount of time you spend fighting blocklists as your source address gets incorrectly ignored as a potential spam source.