The tl;Dr of this article is to email a one time login link to your users instead of having them enter a password, similar to how you reset a password on most sites.

The main reason sites don't this is because it's a bit user unfriendly. I think a reasonable compromise is to use login with Facebook or Google so you never have to worry about passwords. There are downsides of course (user privacy concerns, dependent on third party platform), but since Persona never took off I think it's the best option. When I ran a user facing webapp I offered signing up with email/password as well as social network login, but encouraged people to use the latter.