First of all, there are a lot of question marks here. What branch were the troops from? Where were they stationed? Are they reserve? Did they even see combat? What kind of rankings did they have? Were they all from the same brigade?
I believe the war could've been handled differently as well. But hey, that's war.
(a) How would you know what the troops are doing there? (b) I might be inclined to agree with you on the civil war argument. I mean, if anti-American Sunnis are killing anti-American Shi'ites -- how much sleep can you lose? But the problem is that this creates instability and instability is usually pacified by a dictator. We can't afford to have a tyrant like Iran's Ahmedenjad come in and take over the country or worse, a mullah rise to power. Remember, the Nazis didn't become dangerous until they took control of a country.
You're right. We cannot consider ourselves safe until we engage terrorists everywhere and establishing a "city upon a hill" -- a functioning democracy in the Middle East will provide an opportunity for this to happen. When civilians in other Muslim countries see Iraq's freedom, economic growth, technological advancements, social reforms, political legitimacy, and the like, they will be more likely to embrace it. Right now, those oppressed Arabs in other countries don't see democracy as the shining beacon that it is, and instead they are turning to terrorist organizations like Hamas and Hezbollah. As much as any other war, this is one of hearts and minds. And it starts by succeeding in Iraq.
How much freedom do you think you'd enjoy under Islamic law? THAT'S how I'm protecting your freedoms. If we don't succeed in Iraq, it will embolden the terrorists, be used as propaganda that America is a "paper tiger" (bin Laden's words, not mine) and will actually create more terrorists. More terrorists = threat to your freedom.