ProCourse is actually in the middle of a project like this for a client that is willing to let us open-source the work.
https://github.com/procourse/discourse-sms-authentication
The idea is not to use SMS as a password, but to simply replace the sending of emails with sending SMS through Twilio, Africa’s Talking, and Braze campaigns. The first two are currently implemented and seem to be working well. The last is currently in development.
The concept is to hide the email address on sign-up and fill it in behind the scenes with addresses that mimic the phone number: phone+555-555-5555@example.com. That way Discourse still works with emails if it needs.
But then we tie into specific events (user creation, password update, PM sent, mentions, etc…) and send SMS notifications on top of the email. But since the email is going to the aliased email, the user never has to deal with it.