I've done the same thing in a few prototype-style apps I've built too. Not only do you not need to store passwords, but you can just ignore a whole area of UX.

Enter email to signup -> link gets emailed. Enter email to login -> link gets emailed.

I use JWT for this and it really makes it easy to get started on the part of the project that matters... and sometimes (not always) I think it's probably going to be fine to leave it this way.