I don’t think it has. I think we were better off with Saddam in power. Let’s compare then and now:
Then: Iraq was fully under Saddam’s thumb, but we had him contained, not to mention his military was weakened by a decade’s worth of sanctions. Still, nobody operated outside of his control in Iraq - including terrorists. There is little evidence that terrorists were operating out of Iraq in any meaningful way.
Saddam wasn’t much of a threat to destabilize the region, since we were keeping a close eye on him, and his military was weak. While he had invaded neighboring countries in the past, he’d only done so having, or believing he had, our OK. There was little chance he’d try anything like that particularly soon.
We believed Saddam had biological and chemical weapons, but even if he’d had them, that isn’t the sort of thing that you can use as the backbone of a war of territorial conquest. He supposedly could have used them against nearby countries, but at high cost, and to no gain for him.
The U.S. military had a permanent force in Korea, and some minor commitments in Bosnia and elsewhere, but mostly was available for the next war, wherever it might be.
Now:
There’s no Saddam, and no WMDs, but according to our own generals, terrorists are operating in Iraq. We have 139,000 troops there, along with another ~20,000 allied troops. But that’s not enough to provide security and maintain order in a country that large, so there’s plenty of room for terrorists and criminals to operate. The chaos in Iraq could have a destabilizing effect on other governments in the region.
Meanwhile, much of our military is tied down in Iraq, leaving a greatly reduced force to respond to threats elsewhere in the world. And there are threats aplenty, most notably from North Korea, but they’re hardly the only problem.
I really can’t see how the U.S. is better off for having invaded Iraq. Can anyone enlighten me?