Oil is just a secondary reason for war, if at all. If we had just gone to war over oil, we would have said to hell with everything except the oil-rich regions. Instead, we're helping out the oil-poor Sunnis against the oil-rich Shiites. The greater reason for the war in Iraq was partially that intelligence at that point believed a legitimate threat existed from Saddam. More importantly, the extreme idealism of the neoconservative movement led it to believe that toppling one unpopular dictatorship in the heart of the Middle East could set off a wave of democratization.
Would we have said hell to everything but the oil rich regions? The American public can be sheepish at times and follow our leaders, no matter how incorrect and misguided they may be, but they would never go for that reason and say okay to war. The anti-war movement would be 10X greater if they just outright came out and said we were only going after oil rich regions.
BTW, that legit threat was found to be a lie early on in the war. Powell himself told Bush that there were NO WMD's, and when Bush told him that he was wrong and he was sticking with his story Powell resigned. That legit threat was treated just like 9/11 is now. A serious matter used to rationalize an unconstitutional war, though the matter has nothing to do with it...it's just a use of propoganda.