I would write "open-and-shut cases"

Yes, it should've been hyphenated if both of us were getting paid to post here. You have brought up and excellent example though. The hyphens do nothing in your version. Not a thing! They're just there to fulfill some silly rule. The hyphen in "rubber baby-buggy bumper" does help slightly. But since both phrases are pretty much frozen, I don't think that the hyphen(s) would do much. And if you haven't seen this quiz yet, take it ...

http://quizilla.com/users/BaalObsidian/quizzes/How grammatically sound are you?/