Where we needed troops in Iraq, was an extra 100,000 along the Syrian border (from the very beginning of the war) and an extra 100,000 along the Iranian border (from the very beginning of the war).
The MX division was manning those fronts, so to speak. That's US warfighting doctrine... we can fight up to two wars with conventional units, and as many others as are necessary with nuclear ones. That's why China, for all its bluster, did not take advantage of our commitment in Iraq to conquer Taiwan, because they know we would be forced into a nuclear response.