I have came across some apps that does't do passwords but uses some alternatives to log users in.
Login Links: Sends one time login link that expires after one use or after some time (Usually within couple of Hours.)
Entry Code: A 5-to-6 Digit One time code that users gets via Email or SMS and they use this code to Login to the app.
Other way is to Use Third party authentication like facebook or twitter, but in order to do that, said product must have already built trust among their users and even after that many users will not be comfortable of using their social logins.
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