For example, you can't play poker locally because you could see everyone's hand. With this, the hands can be displayed on the player's phones. This goes for a lot of board games.
I agree that Skyrim should skip the second screen, but imagine using the iPad as the map from CoD or BF3 - issuing commands to squads via the iPad while they control their characters with normal controllers.
I'm remembering commander mode from BF2 and thinking that if I had a second screen for something like that, I'd be in heaven.
Even if the functions of the "start" screen (squad/team/comms/weapons management) were relegated to a second screen, I think it'd be a big improvement. It's a lot easier to switch context in the physical space than it is to flick between screens with input lag and the fact that it completely obscures your view. It's a modality issue. You can't effectively divide your attention.
I think I'd need to see an implementation that wasn't just a rehash of a board/card game I can play quite well already thank you very much to believe it.