"... I doubt if the situation in Iraq now would have been any worse, and it would have been much easier on the US."

I didn't really address this.
I guess there is a hard way to answer this and a simple way to answer this. First the simple way, I guess. Washington DC has highest murder rate of any other American city. And our murder rate is dropping. Let's say the DC murder rate doubled to 100 deaths per 100,000 per year. What should we do? Leave it to it's fate? Maybe they will learn how to get along with each other?
Baghdag has around 6 million people. At 100 murders per 100,000 that is 6000 per year or 500 murdered per month, 125 per week, or 16 per day. It is not this bad in Baghdag. With country pop of 25 million at 100 per 100,000 that's 25,000 murders per year. Of course Iraq and in particular Baghdag in chaos- similar to say LA with gangs in a drug war way out of control. It would like gangs that are attacking police stations, cops are fleeing, gangs are ruling the streets, etc. It's like a continuous LA riots that followed Rodney King trial.
Now, living in peaceful Torrance Califorina in the rare instance I hear semi-automatic gunfire going off, I get a bit nervous, and having this happen more much often and having mortars going off is not my idea of picnic. Or having the National Guard at the local K-Mart for a couple days is interesting and even somewhat assuring following the Rodney King. Having cars burning and gangs roaming, would remind me too much of Paris- disturbing and dangerous.
Now, the terrorist are directing their attacks against anything which can be seen to be helpful to Iraqis having peaceful and prosperous country. They want to cause maxinum misery with the few resources they have. This is slightly different behavior then typical French or Rodeny King rioters. Even the rioters have some sense honor or loyality to country- in their insanity they still generally have some red lines.

Ok, now more complicated/harder part. I'm just going to list them. We were already in Iraq- in Kurd area. Iran is a problem. Middle east is geopolitically important. We have to set good example in terms of what is internationally acceptable. We have allies in the region that demand better behaviour from their key ally. Saddam wasn't important nor really the problem- others who replace him including his children could more crazy than he is. Did mention Iran and their making nukes and their ties to terrorism? Syria and their ties to terrorism. Cooperation in fighting terrorism by mostly soft type power- and covert/police action [depending on countries in region- perhaps strangely Syria this even includes]. And countries which could do things which are hostile to American/global interest seeing unwillingness for America "to get dirty" may encourage them to see America as paper tiger- if we aren't willing to fight this battle how much can other nation depend upon America in other potential battles.
And there are other reasons which I could list, but I'll mention one other and that is the the US miltary is a stronger miltary force because of it's experience in Iraq. Anyone who knows anything knows this, people who say otherwise simply don't know history. Anyhow the result is that whose want want to start a war, will probably decide that 10 or 20 years from now would a better time than the present or next 5 years. Iran might not be this intelligent but these guys are pretty stupid in comparison to other countries.