I don't think it's a bad idea. Imagine something like a google hangout where thumbnails of 4 of your online buddies are stacked on one side of the screen (like one of those side-screen modes for Apps in Win8). It wouldn't occlude too much of your view. And imagine that each thumbnail could be showing either the videofeed of them playing, or a live shot of the gameplay from their system. Also imagine that none of you need to be playing the same thing, so if one friend playing Just Cause 3 says, "Oh man, the craziest shit just happened, you guys have got to see this!" everyone can pause their game, select his game view, go fullscreen and watch as he scrubs back a few minutes to show you a replay from that had been automatically saved by the system.
Or imagine you're playing a game and your sister tries to call you on Skype. Since it's linked to your GamerTag you get a ntification in the middle of your game. Instead of having to save, close the game and call her back with the dedicated Skype app, you can just hit the button to accept and your game pauses in the background and a video stream from your sister pops up to take over most of the screen. You can talk like that, or if she just wanted to chat, you can shrink he box to one side and keep playing.
Or imagine you're waiting to watch a baseball game that has been rain relayed. They haven't cancelled, but they're spending a half hour waiting for things to clear up. In that case you can pop into CoD, or whatever, and pin a live video feed from ESPN to the corner of your screen so you can see right when they get ready to start playing.
I can think of lots of uses.
