It has never worked for me on iOS. Everyone kept saying "I can just share the password" but the prompt never popped up, and there was no way to do anything.

IIRC it only works if you are on their contact list. And I think you need to be in the settings app. Something like that. It's a handy feature but Apple could make it easier to understand, and they could do way better communicating why it isn't working, when it does not work.