In Oman the Sultan, said "defeat the rebels, - so that development can begin."
In most UK insurgencies the basic guidance was "defeat the rebels - so as we can organise the peaceful transfer of power to a democratic political process."

And in both of those cases, the populace's position was "throw out the Despot so that we can replace it with govnernace who's Legitimacy we recognize, who treats the populace with Respect; where the people can find Justice under the law; and where once again the people can have Hope."

I'm sorry, Great Britain is the best BAD example of COIN theory in the past 200 plus years. Their entire model is based upon sustaining in power forms of government over the populaces of others that recognizes its priority mission being to support the National interests of Great Britain. That, my friend, is not COIN. That is Colonial Oppression.

A great political cartoon would show Uncle Sam staring into his bathroom mirror preparing for his morning shave, and seeing King George staring back at him. The caption would be along the lines of :

"Holy S..t, I have grown up and become my father."