I think the discussion is going around in a rather unproductive circle.
The problem with this formulation is that AQ is not leveraging "insurgency" at all, if we define insurgency as conflict between governments and the populaces they govern. They've tried, but they've failed. What AQ does leverage effectively is a widespread (but not universal) perception of Western oppression among Muslims, particularly resentment toward direct "infidel" occupation of Muslim countries. When deprived of this stimulus - such as after the Soviet withdrawal from Afghanistan - AQ's relevance and support decline rapidly. Paradoxically, this is when they are most dangerous: because they need foreign intervention to survive, they will lash out and attack in hopes of provoking that intervention and restoring their relevance. That's no reason to give them what they want.
SE Asian Islamic insurgent/separatist movements are generally not that susceptible to AQ manipulation mainly because they and their popular support base are focused on local issues and not really concerned with the pan-Islamic narrative or the perception of general oppression of the ummah that AQ has to sell. There are of course a few exceptions to that rule, and local organizations will cooperate with jihadi groups to the extent they deem convenient, but in any broad scale sense SE Asian Muslims are concerned with local issues and don't particularly care about foreign occupations in Iraq or Afghanistan, about Palestine, etc.
I agree that "CT" as we know it now should only be one part of any effort to address terrorism and its underlying issues. It remains an important part, and it's natural that it's the part that will dominate military discourse because it's the part of the program that the military, along with the intel and LE communities, is responsible for implementing. Whatever we think of causes and whatever we can do to alleviate causes, it has to be clear beyond doubt that people who attack us or our allies, plot to attack us, or shelter those who attack us will be subject to direct action, wherever they are. No nation can condone or accept attacks on its territory or citizens, whatever the cause.
To a large extent I agree, but I think your assessment of the "primary purposes for action" is flawed in a way that leads to some very dangerous conclusions. If we assume that AQ draws its sustenance from the relationships between Muslim governments and the populaces they govern, there's a tendency to try to affect causation by trying to influence those relationships. That's both wrong and dangerous: AQ draws its sustenance not from relationships between Muslim Governments and those they govern but from the perceived relationships between the Muslim ummah and the non-Muslim world around it. Trying to interfere in relations between Muslim governments and those they govern will be ineffective and probably disastrous: we have little influence in most of these relationships and we have no credibility as a mediator. Neither populaces nor governments want us involved and trying to push our way into the picture uninvited just reinforces AQ's narrative of Western interference. That doesn't mean engagement is never a good idea, but it should be multilateral whenever possible and it should be as requested by local groups with a credible claim to speak for the people, not initiated by us.
We can effectively deprive AQ of much of their impetus simply by not invading or occupying Muslim territory, and my minimizing our overt interference and military footprint. We have to understand that if we do this we will be attacked: AQ will try to provoke a response that they can manipulate. That doesn't make it any less important. Trying to change the patterns of governance in the Muslim world is both futile and dangerous. We shouldn't obstruct change, and we should work with it as it occurs (as we've been doing) but trying to compete for influence over Muslim populaces or trying to appoint ourselves as a mediator or champion of the populace is going to snap back in our faces in a major way.
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