History argues the opposite. Take, for example, Afghanistan. There, with massive covert support from the US, the Soviet dictatorship was removed. Then, the US abandoned the region to sort itself out. This left a power vacuum that was filled by the Taliban and created the safe haven for Al Queda.
Politics, like Nature, abhors a vacuum, and out of chaos, it is rare that anything but a thug state emerges to make things stable. Given the history of Mesopotamia since the time of Abraham, what makes you think Iran, Syria, and Saudi Arabia would be content to let things settle out in the strategic breadbasket of the Middle East?
In the case of Iraq:
1. Relatively flat terrain with easy surveillance.
2. A no fly zone with sea-launched missiles to shoot offenders down.
3. A continuation of the struggle between Sunnis (Syria) and Shias (Iran) making everything else a footnote.
4. A land locked country with nowhere to go.
5. Who cares if they fight and kill each other?
6. No reason for Al Qaeda to be there because there are no infidels to kill.
7. Chaos that ensures no sophisticated organization to threaten us.
Of course, we're there now and it is all too late for this. But I read military history and I don't know a General alive today who would have put soldiers into Iraq to catch bullets -- unless that General was under direct orders to do so by the Commander in Chief.
I will say it again. We DID win the war in Iraq years and years ago.
The terrorists were elsewhere at the time.
And then we decided to stick around.
Now, we urgently need 200,000 additional troops, at the very least, to police every single square inch of Iraq -- and protect each other. Our enemies are invisible until they attack us. Ever see that movie Predator? That's what its like for an American soldier to fight a guerrilla war. It sucks.