BUT...
Islamic principles may be the basis of the laws of the nation without the country as a whole being an Islamic State. There's a lot of talk about Democracy in Iraq, but the US government has been very careful to make it as much a republic as possible.
Look at the founding of the US. Virtually all the Founding Fathers were quite religious, and many of the laws were based on christian ideals; yet they had all been burned by the State religion at one point or another. They were all wary of authority vested in a sovereign, whether it be a royal or (the supposed representative) of a heavenly one. They set out to create a weak central government. Do you notice the Iraqi governing body is called a "Parliament" but that the laws are set up to prevent a majority party from taking the whole thing over? If one faction tries to take over, the other two will stop it. Except everyone knows, of course, that one faction will try to stop it, and the Kurds will just withdrawal and set up their own little principality-which would force the Turks to get involved. And NOBODY wants the Turks to get involved.
Don't forget too that about 3% of the population is Christian, which doesn't seem like a lot, except like the Jews in most of the West(0.5% of the US population) they've put a lot of emphasis on education, and operate at the highest levels of government and society (no Z.O.G. jokes, please). A caliphate would force most of them to emigrate, and while we would certainly benefit (because most of them would try to come here), it would only hurt Iraq.
"Islamic Principles" is just that.