if you are supposed to build an app, which absolutely needs a password, what would you do?

don't blame that developer. blame Twitter for doing lousy job. Look at how FriendFeed handles Password requirement by giving Remote Key.

Developers are not happy to ask users passwords in text format. They simply don't have other option.

I'm not blaming the app creators. I think Twitter and other sites need to learn from FriendFeed.