In general agreement, and why I and others think we need a strategic context that consists foremost of desired ends. Then we can assess if suppressing an insurgency is in our interests or not based on criteria that are bigger than the local conflict.

I'm specifically speaking of U.S. interests, but clearly most of our allies and partners share many common interests that will facilitate collaboration.

While you may be right about riding a dead horse in some cases (Karzai, Maliki, Marcos, etc.), there is strategic risk to simply pulling the rug out from their feet. Beyond local repercussions, over time it sends a message that the U.S. is a fickle friend and will weaken our alliances. Based on that aspect, and I'm sure there are others since it is a tangled web, I don't think dropping someone like Maliki is as easy as you make it seem.

This is not what the US's mission is these days, but yet the SOIN that so many think of as COIN is derived from the lessons learned from those type of operations.
What is the U.S. mission today? We understand the difference between FID and COIN, so sticking specifically to COIN, our mission in Iraq and Afghanistan was to protect/defend the fledging governments that we deemed legitimate. The war in Afghanistan was tied to fighting to the al-Qaeda network, so in my view the intent was legitimate, but in practice fighting al-Qaeda became a side show at best. We started calling every low level Taliban IED producer a high value target and instead of targeting the real networks that threatened us we almost completely transformed the fight. I'm not touching Iraq at the moment, I still can't talk or write about it without spitting venom.

How would the US benefit in the long term from helping some client regime suppress the symptoms of insurgency in their country?? This is what creates and thickens the vectors of transnational terrorism back to the US. This is what validates and enhances the UW operations of AQ and now ISIL as well.
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. Obvious, maybe in only hindsight, but I don't think so, we needed to develop different options. Let's not forget, AQ attacked several time before 9/11 and then of course the tragic attacks on 9/11 long before we invaded Iraq and Afghanistan. Our actions made have made the threat worse, the jury is still out on that, but the threat was there before hand.

We have to stop thinking about insurgency as if we were still a colonial power. Until we can do that we are doomed to fail. It is not the fault of our tactics, though bad tactics do not help. It is the fault of our poor strategic understanding of the problem and our poor strategy for approaching these problems in general.
What makes you think we view COIN as a colonial power?

Once one shifts to thinking about these types of conflicts in the proper framework it becomes clear why legitimacy is the central issue, not a side issue. A side issue for SOIN, but central for COIN. One cannot create legitimacy in some other government, and one cannot grant legitimacy to some other government. The more one interferes between a population and their government, the less legitimacy that government has. SOIN operations are typically a deathblow to legitimacy.
Legitimacy may or may not be the central issue depending upon our strategic goals. Furthermore, I think globalization and information technology has fundamentally undermined the folk wisdom that all politics are local. The overwhelming number of foreign actors, both state and non-state, in many of these conflicts (not all) requires we reframe them. Local issues may have provided the tinder that allowed the fire to start, but once it started it took on different characteristics, meaning addressing the original underlying issues won't solve the problem.

The reality for the US is that our interests are better served the less we interfere in these foreign revolutions. I was at a meeting with several successful business executives and a couple members of the state department. For state all corruption is bad. One exec commented that for many places, corruption is how taxation occurs where there is no effective legal taxation. The State reps had a fit. Likewise, insurgency is often how democracy occurs where there is no effective legal means to shape governance. That truth makes people have a fit as well. But still truth all the same.
Of course our business execs would say that, that is how they facilitate deals in many foreign countries. I don't disagree it is part of most cultures, but it is still one of the biggest drivers of conflict in many countries. A government that steals from its people is not legitimate. This is another myth, like all politics is local, that NPS COIN professors like to promote. It matters, and in many locations it matters enough to fight.