Maybe we are being pessimistic…after all, we thought that we’d march in to Iraq, and be greeted with flowers. set up a friendly government, and all would be well! So, we were wrong…it is looking that Iraq is more like Yugoslavia every day. Both “nations” were artificial creations of the 1919 Treaty of Versaillles, and both natuions lack legitimacy (in the eyes of their “citizens”). Well, why try to hold this mess together? Months ago, I argued my thesis that Iraq ought to break up, possibly into three states. Think about it:
The North (Kurdistan): at least the Kurds don’t hate us…let’s reward them and set up a government here. We can arm the Kurds, and protect them with air support. A fully armed Kurdish army would be an excellent ally against the Baathist fanatics and their allies.
Baghdad and central iraq: we should cut a deal with the Sunnis: we leave them alone, in exchange they don’t attack us. I suggest that we could get out of this region in 2-3 months.
The South: we should take advantage of the fueds between the various Shia factions, and cut a deal with Al Sadr: the deal will be simple…he gets control of his precious mosques, and the Shiites get to run their own affairs…just make it clear to him that any attacks on US/British forces will be met by the toatl destructions of these shrines that the Shias love so much.
Alawi: give him a tiaket to Switzerland, and forget tha nation of Iraq. Better it should disappear…who with any sanity mnours Yugoslavia? 
For one thing the US promised to maintain a united Iraq… whatever that means.
Now for some serious reasons… if they separate Kurdistan that will mightly piss off the Turks. That might even embolden Turkey to just take over northern Iraq to protect Turkish interests and Turkish ethnics.
Iran would certainly hold a strong sway over Shi’ites. It would be like giving away a piece of land to Iran. I don’t think that is too bad… but the US seems to hate Iran and vice versa.
The Sunni and the Shia aren’t going to easily go their separate ways… expect massive fighting and civil war in order to determine who keeps more stuff.
So the US, in my view, is trying to keep Iraq togehter for the above reasons and the Kurds in Iraq in order to have a 1/3 guaranteed pro american Iraq. Especially in a future Congress if they manage elections. Kurds can help sway future Iraq governments from being anti-american… or at least to be “friendlier” to american interests. An independent Kurdistan isn’t worth much to Washington.
Not entirely true WRT Yugoslavia. The idea of a unified south Slavic state (yugo means “south”) existed at least back to the 19th century and there were, and even today still are, significant numbers of people who consider(ed) themselves Yugoslavs first.
Quite a number of people in Serbia do, in fact. Their country is in far worse shape now than it was in the Tito era - far, far worse.
The obvious parallel between Yugoslavia and Iraq might be extended further. It presents the danger that if the unstable political order in Iraq ever breaks down entirely, we might see a Yugoslavia-style civil war, complete with “ethnic cleansing” atrocities. Only worse, because ethnic hatreds would be complicated further by religious ones – and by the presence of Iran and SA on the borders. 
There are some significant problems with the OP’s analysis. The most substantial is one that is extremely widespread: seeing a sharp demarcation between Kurd/Sunni/Shiite parts of Iraq. In reality, these three populations are so mixed that any partition of Iraq will inevitably be very, very bloody. It would quite likely be as bloody as the partition of India/Pakistan, albeit on a smaller scale, and have even more tendentious long-term consequences due to the uneven distribution of oil reserves in Iraq. India and Pakistan are still perpetually two steps away from war over a barren mountain range. Can you imagine if the Kashmir had oil underneath it?
Second, partitioning Iraq has consequences beyond Iraq. The states neighbouring Yugoslavia are, for the most part, quite stable. This is not the case of Iraq’s neighbours. And independent Kurdistan in what is now northern Iraq has well publicized ramifications for Turkey and Iran, which also have significant Kurdish populations. An independent Shiite-majority state in what is now southern Iraq would have less-well-publicized ramifications for Saudi Arabia and Iran.
Finally, I don’t think that we should suggest that Tito or Saddam’s rules were good. They were simply less bad than certain high-probability alternatives. A lot more planning and preparation, and specifically a lot more well informed planning and preparation was mandatory if Bush’s Iraqi Adventure was to have turned out well.