Microsoft's divisions (most notably Xbox) have always had a huge dilemma: Do we act in a way that's best for our division, or do we maximize value for MSFT. From my time at Xbox, I can say with certainty that the implied actions for each choice are often not the same.
I think (and a lot of other would agree with me on this) that the Xbox division within Microsoft is the most customer-centric of any company in the entire world.
The people at Xbox are die hard gamers who really want to help you solve your problem whatever it might be. I don't know if spinning off one of the best divisions would be such a smart division specially when it is already profitable, unlike Bing.