The key point in why I don't think it is helpful to consider COIN war (even though I believe that insurgency typically is war for the insurgent); is because COIN is waged against one's own populace. The techniques, tactics and procedures, the very mindset of war are completely counter productive to a government resolving a dispute with an armed rebellion that enjoys a broad base of popular support.
Now that is illogical unless you somehow believe that COIN is bloodless.

Name one insurgency that has been "countered" without some use of military force.

You seem bent on equating what I have said with the idea that COIN is purely military. Nothing could be further from the truth.

You also seem intent on believing that our foreign policy should be directed on behavior modification of various governments to match our value system. Good luck with that.

Tom