Distillations are valuable up to the point that they lead to over generalizations that hinder clear thinking.

I stop at the three categories I settled at because I believe that to combine those together I begin to lose distinctions that are essential to COIN process. Now, if I am merely a "counterinsurgent" or conducting "counter guerrilla" operations, it does not matter if I lump these three distinct categories of causal motivation together, as all I want to do is destroy those who dare to challenge the government with illegal violence.

It is this type of thinking that leads to combining the rural, largely apolitical, resistance insurgency in Afghanistan along with the highly political revolutionary insurgency of the Taliban leadership in Pakistan. We then go on to engage one in hopes of curing the other; conflate them as a monolith; and generally end up applying the wrong solutions to the problems, or applying a potentially workable solution to one end of the problem, while addressing the other end in a manner that neutralizes the good effects and makes the entire problem worse.

If you consider the real success behind the surge was that Gen Petraeus essentially recognized these three distinct segments and tailored his approach to each. He left the Kurds alone and did not press the issue of the central Iraqi government exerting its sovereignty over them. Satisfied, this largely took them out of the fight. For the Sunni it was largely a resistance. They had held power, and were now excluded and in danger of being dominated by a Shia/Kurd government. By reaching out to the Sunni and addressing their concerns at being excluded he began to take them out of the fight as well. For the Shia it was a mix of resistance and revolutionary; wanting the foreigners to leave and to exert their own dominion over the government. (AQ really was not part of this. They were never "insurgents," they were foreign fighters who traveled to Iraq to inflict pain on the West and advance their own political agenda. The majority of those foreign fighters being members of nationalist insurgent movements (revolutionary) in the various Arab states they came from (Saudi Arabia, Libya, Tunisia, Yemen, Algeria, Egypt, Syria, etc). AQ was conducting UW with the Iraqi populace as well.

If we would have continued to apply a "one size fits all" approach we would still be mired in high level combat there. Surging troops and pop-centric tactics are all ancillary to the larger strategic understanding of the problem. As is so often the case in insurgencies and interventions, often the greatest aspect of the cure receives the least credit.