WRT Iraq - seeing as how we have moved off Afghanistan:
When the US was asking its own soldiers how many bodies the Army would require to secure Iraq it seems to me that the Army proposed a number that effectively denied the US any opportunity to involve itself in Iraq at all. The Army effectively came back with a "you can't do that, you can't get there from here" solution.
Whether the US was right or wrong to involve itself in Iraq (I think it was right) thus ultimately became immaterial. If the US Forces, the most powerful such organization in the world, was saying that "there ain't nothing I can do" then the entire world order was put at risk. That order is ultimately built on the basis of coercive force. If the US wasn't powerful enough to coerce a place like Iraq how likely was it that the EU, Russia, China or India were going to be effective ( even if we wanted them to be so ).
At the same time the US army, IMHO, really didn't want to get into the game that they are in. It could be seen as a self-serving statement, "we can't help you" from an Army in which many did not want to get into the Small Wars/Constabulary/Co-In/Peace Support/Peace Keeping/3-Block War/Imperial Grunt business.
Unfortunately the US administration, the UN and the world at large need that capability ( not just from the US and not solely from the US ). If the US Army could beg off as being incapable then that allows every other army to beg off. That ultimately isn't good for international security, for the average citizen or for commerce. Then we quickly run down hill to the post-Tito Yugoslavia on an international scale.
Whether the US Army wanted the job or not, or whether it was capable of the job or not, the US needed the US Army to do that job. Just as we need the Brits, Aussies, Canadians, Dutch, Indians and all other armies to do that job.
It is possible to argue about where and when and how and under whose authority such troops should be deployed. But that capability must be held by the international community. "We can't. We don't want to." can't be allowed to stand as an answer.
The fact that the US Army then has had to learn on the job and adapt in place has resulted in mis-steps but the shift in that Army was necessary. Iraq was as good a place as any for it to make the adjustment. It could have been any of a number of other countries.
I have heard the argument "Why pick on Saddam? There are plenty of other targets out there." The answer is the same in any target-rich environment. You have to start somewhere.
He was victimising his own people, was a proven threat to the neighbourhood, had some nasty friends with vicious tendencies, was looking for opportunities to make a big splash on the international scene by buying up some nasty technologies and failed to honour his commitments - all these seem perfectly rational reasons for acting on him first. It was his misfortune that, if he truly had no WMDs and didn't ship them back to his suppliers via Syria, he lied so many times that nobody believed him when he said he didn't have them. NOBODY believed him. Not the Yanks, Brits, French, Germans, Russians, Chinese, Canadians or the UN. They disagreed on what to do next but nobody believed him.
The fact that Iraq sits smack-dab in the middle of the lines of communications connecting Pakistan and Afghanistan to Algeria and Morocco, not to mention Turkey and the Caucasus also made it a critical target that needed to be in the hands of a benign, if not friendly, government.
The role that Iraq, Iran and Afghanistan play currently is more akin to the role that Port Royal, Jamaica; Chesapeake in the Carolinas; and New Orleans played in the 17th and 18th centuries. They were havens for pirates and smugglers that occasionally operated under a commission from any government that would by their services during times of tension. Not everybody operating for the Islamists is operating out of religious conviction.
