I think it's more complicated than that. It's not just ensuring our interests, it's ensuring that hostile interests do not benefit. If we were to simply wash our hands of Iraq, for example, it would mean conceding Baghdad to Iran, and probably losing much of northern and western Iraq to ISIS' new "caliphate." This would pit fundamentalist, largely Wahhabi Sunnis against the world's most powerful Shi'ite regime. Oh, and then there's the Arab-Persian thing.
Now, maybe you say that's what we should do, just walk away and "let them kill each other." But there are problems with that:
1. Oil. This region contains over half the world's known oil reserves. Together, Saudi Arabia, Iraq, and Iran possess 500 trillion barrels of oil. That's good, because the world uses almost 100 million barrels a day. The United States accounts for 19 million of these, but the rest of the world is catching up. So like it or not, we need that oil. It is a vital resource essential to our economy, infrastructure, and way of life. We live in a petroleum-based society. So we have to have that petroleum. If not us, who? The Chinese? The Russians?
2. Israel. Israel is a close ally of the United States, the Jewish lobby has a great deal of influence in Washington, and the Jewish vote is crucial in many states. The United States cannot and will not abandon Israel, nor is it in our interest to create a situation that threatens Israel's security, as the establishment of an ISIS-controlled state certainly would be. Again, this is a like it or not situation. I make no comment as to the rightness or wrongness of this policy, I am merely stating the reality of the situation.
3. ISIS. This is a dangerous group that rose up almost out of nowhere and quickly seized control of the Islamist movements opposing Assad in Syria, and in two years they have become a de facto state. They already control several major Iraqi cities, including Mosul, and many online sources (although tellingly not the mass media) are reporting that people are happier under ISIS rule. Granted, it's early days yet — I'm sure many Iranians who were happy with the revolution in 1979 later came to be less so. But if these reports are true it does not bode well for the central government in Baghdad, nor for the United States. An ISIS-controlled state, recognized or not, would have the potential to become a major training ground and staging area for attacks on the United States. Not to mention the threat it would pose to #1 and #2, above.
I do not disagree with the assertion that the United States' national interests are directly impacted by events in Iraq. I just don't know what I would do about it. It's easy to coach from the sidelines, but the reality of the game is so much more complicated. This is one time I'm glad I'm not president!