I agree with Wilf and Ken. There is a military aspect to COIN, or else it would not have reached the stage of armed conflict. Yes, State and NGO’s play an important role in COIN, but that is there role, not the Army's. The military's role is to fight the insurgents armed force and there means of supply and communication. I feel that stating that insurgencies are always about the population is flawed. Some insurgencies derive there strength and supply through the population but some do not.
The big difference in COIN and HIC in my mind is that COIN has an aspect of Law Enforcement to it. I wonder if having some sort of US Gendarme would pay dividends?
On an almost unrelated note: I feel strongly that reducing the DOD trend of micromanagement would pay big dividends in creating thinking, better fighting soldiers in both COIN and HIC. Creating effective and productive infantry is a big part of this as well.

Reed
Sorry for the scattered thoughts, working way too many hours.