If MS let them split and build up 343i(founded 2007) to continue the Halo series it doesn't look to me as if MS really played hardball here with Bungie's creative interests. Why shouldn't MS be interested into new IP developed by people with a proven record?
Therefore I think the whole thing is more motivated with IP/Control/Money.
Naw, I just got the timeline wrong. By the time Halo 3 was finished, Bungie had already been making some noises about how tired they were of working on the Halo franchise. It's all they'd been working on for almost a decade by the time Halo 3 was released to the public. Halo was announced in 1999 with development having started a year or two prior to that.
Bungie were just very burned out on working on Halo, it was the last thing they wanted to continue working on, at least without taking a break from it.
As you mentioned they had to stick around to fulfill their contract obligations. MS knew that, Bungie knew that. Had MS allowed them to work on something other than Halo, after Halo 3 as I said, there's a good chance they would have stayed with MS.
Unfortunately, that wasn't something MS could have allowed. Halo is far too big of an IP to let sit idle. It's also far too big of an IP to allow for the chance of substandard development, hence the creation of 343i.
It's also completely understandable that Bungie were sick and tired of working on the same IP non-stop for that long. Look at their past development history. They've aways mixed things up to allow their creative juices to flow. Marathon - FPS into Myth - RTS into Oni - third person action game and then back to FPS with Halo.
I'm not sure it's the direction they are going but it seems like Destiny is going 3rd person instead of first person. As well as with a large universe where they can tinker with ideas beyond just straight up FPS style of gameplay.
They did say they would like to revisit the Halo universe at some point. But only after they've had time to develop some other things first because they were basically tired of working on Halo.
If the Halo IP had followed Bungie, it likely would have sat idle with no one working on it for 10 or so years. Which would have been a problem. As you can bet whichever publisher they signed with would start to put increasing amounts of pressure on them to make a Halo game when the last thing they want to do is make a Halo game.
Regards,
SB
It makes you wonder if they've licensed an engine from Crytek, Epic, or someone else. 
