quillsinister,
The US did give half of Germany to the Soviets no questions asked, and they did give Eastern Europe to them without a fight at the Yalta conference. The situation is very similar, communism only took root in East Germany, Czech, Hungary, Poland etc because the Allies didn't oppose it. Those countries all had democratic governments in exile that tried to reestablish themselves but were pushed out by the Soviets. So here is another history lesson. You don't understand several things thats skewing your judgement on the matter:
1) Islam is not monolithic. I know everyone seems to want to think the "Shiites" or the "Sunnis" are all either with or us or against us but thats is just not true. The Iraqi Shiite population will not simply side with Iran because they are Shiite and we are not. Thats like saying German Protestants would side with America over France because it is Protestant and France is Catholic. These people have Iranian leanings because for twenty years while the US was supporting Saddam and then the Iraqi National Congress these people were being supplied, trained, and harbored by the Iranians. They are political allies with them, and as we know once situations change political allegiances can be broken by better offers. Iraqi loyalties are based on tribal loyalties, not religious sect, most tribes just happen to be of the same sect.
2) Iranians are not Arabs. They are Persians. So they have a different culture than Arab Shiite Iraqis who they have more or less been at odds with since the 12th century. Its like the culture of Mexico and the US. Kinda the same, but big differences. Iranians speak Farsai on the large part, Iraqis speak Arabic. There is no unbreakable cultural bonds between them.
3) America's power is not limitless, but it is hegemonic. That means it holds supremacy over everyone else. The Iranian military and economy is significantly weaker than Iraq in 1991. Iran knows their armed forces would last a matter of weeks against an American attack and so they aren't the Soviets. They aren't going to stand toe to toe with the United States if it steps up to the plate, they are at the disadvantage if the US starts sabre rattling.
4) The United States still runs Iraq, not the Shiite government, thats the point. It obviously wouldn't be wise to just start toppling democratic governments, because hell that would kind of making the mission worse than it already is. But the Iraqi government is paid for, trained by, supplied by, and allowed to survive by the grace of the American government. Now is precisely the time to ramp up the pressure and force the Iranians out before the Iraqi government can stand on its own two feet and support itself.
The point is that nothing is set in stone in Iraq yet. It is better to force the Iranians out now by weakening their internal allies and showing whoever America picks to be in charge that there is more profit in towing our line than theirs. You for some reason think that the Iraqi Shiites are married to the Iranians, but thats not true. Its simply an alliance of past experience and convenience. All the United States has to do is make it less convenient.