You wrote about AQI,
It depends, if we allowed AQI to take over Iraq it certainly wouldn't have reduced terrorism? Allowing Maliki and the Shia to dominate basically made Iraq a proxy state to Iran, so in the end allowing AQI to win would have undermined our interest, and promoting mob rule by imposing democracy to facilitate a Shia take over did undermine our interests.
That is what I responded to in regards to Iraq. We brought AQ to Iraq when we invaded. You add that we also facilitated AQ to gain an earlier toe hold with our no-fly zone. Perhaps, I'll take your word on that.

We argue "interests" to rationalize all manner of activities, like taking down the Taliban government rather than simply punishing it and leaving it in power. We then end up engaged in generation-long campaign that is absolutely counter to our interests.

Many think the US income tax is stealing. People know when their government is operating outside the cultural norms of their society. in some areas people can vote in new government. in other areas they must resort to revolution. These things are self-leveling. When we intrude to skew the results to be what we think is best for us we disrupt their governance. You would not want China to spend a Billion to get their candidate elected as our president. You'd feel that what they did legally and for their interests was a very illegitimate thing indeed. Other people in other countries feel the same way when we label their revolutionary movements as terrorists, and then conduct operations to ensure that our candidate stays in office.

We have lost our way, one step, one decision at a time over the past 70 years. it happens. We just need to shoot a new azimuth and get back on course. We also need to recognize that some approaches to securing and advancing interests that used to work reasonably well are no longer feasible in the current environment. Our archaic and flawed understanding of what insurgency is, why it happens and how to best resolve it is also a major contributor to many of our current challenges. It is why all of our great tactical actions do not produce intended strategic results. We remain drawn along by our own inertia though.