I only addressed this briefly, because like I said, I think the prospect of HRC becoming Secretary of State are pretty slim, but frequent commenter Mike builds the correct case:
You know how NFL teams have quarterback controversies? Or a talented offensive coordinator like Jason Garrett puts pressure on Wade Phillips? Imagine the US foreign policy situation with Hilary and Barack. That’s why I think you don’t appoint Hilary.
Now, I don’t think it’s quite so pronounced; Wade Phillips didn’t appoint Jason Garrett, Jerry Jones did. Also, I think HRC was forced into her hawkishness by her vote in support of the War in Iraq. It was a political argument (not that this particularly forgivable — but it happens), and I imagine she’d be mostly on board with whatever policy Obama chose to pursue. Indeed, CNAS — the think tank with which Hillary’s foreign policy views were most closely associated — has moved further toward the progressive vision of Iraq. Arguably, this is more a reflection of the political center’s lurch leftward on most matters of policy, but the effect is essentially the same insofar as it has yielded views in comity with Obama’s.
All that said, in light of the “3 AM Phone Call Ads” and what have you, the tension would at least be perceived, which would potentially color the Department’s functioning moving forward. In my view, the much safer play if Obama were looking to demonstrate some sort of centrist bona fides would be to appoint a Republican from the realist school like Chuck Hagel or Dick Lugar, though I’ll add this has potential for problems as well.