The breakup of Iraq vs. Yugoslavia

Since the most recent war in Iraq began, one overarching premise has been supported by almost everyone of all political strips in this country and others: that Iraq should remain a single country and maintain its "territorial integrity." Is this really the best plan? Might not the people of Iraq actually be better off if the country were split into three, roughly following its sectarian divisions?
A comparison with Yugoslavia may be instructive. Both countries had deep and ancient ethnic and religious divisions. Both were held together by a strongman/tyrant. When Yugoslavia dissolved, there were cross-boarder conflicts, but once Milosevic was deposed, they have achieved relative peace and stability. Yes there are still problems and the resulting countries are distrustful and sometimes hostile toward their neighbors and former countrymen. For the most part, however, each country and its residents are able to go about their business with autonomy and determine their own future.
I propose that a similar fate would actually be good for Iraq. The British created the country artificially decades ago. At that time, the people composing the population had the same divisions they do today. If Iraq were to dissolve into three autonomous regions: one Sunni, one Shia, one Kurd, would it really be so bad? They would each have their own state and be able to determine their own fates without interference or worry. There would be no reason for conflict.
Negative consequences are possible, of course. A radical theocracy could arise in one of the offspring countries. A tyrant could take control in another. I think the chances of these scenarios occurring are actually less likely now, though, and if either does occur, it will be much easier for the world to deal with, simply because of scale.