All quotes are from Bob,

No one ever said that when faced with a violent insurgency that it would not require violent reactions, only that such violent reactions are not war because the objectives are different than war because the opponent is your own populace and you're going to have to live with them when its over.
You’re trying to redefine war as strictly an activity between States which in my view is very close minded and worse doesn’t conform to reality. Al Qaeda is an external non-state entity that has declared war on much of the world. The fact that they’re partnering with various surrogates in those countries to conduct their own version of through, by and with operations does not change the equation, it is still war.

The essential nature of war is that it is a large scale duel, where each dualing party uses force/violence to compel the other side to submit to their will, and each opponent is subordinate to a rational policy (political or other higher objectives)

Just because the military showed up does not change a civil emergency into war either; though too often when the military shows up the civil government abdicates its responsibilities and the military turns it into war.
Prior to the military getting involved it was a dual between two armed and organized opponents attempting to compel their will through the use of force (and other means, but the use of violence is what make it an insurgency).

The American Civil Rights movement was largely a non-military response with a main effort of addressing the wrongs of government rather than defeating the wronged segment of the society. That was excellent COIN.
The American Civil Rights movement was NOT an insurgency, it was a social movement. True it could have escalated to an insurgency if preventative measures were not taken, but prevention is not COIN, it is prevention and social movement is not an insurgeny. I don’t think you’ll find much disagreement that prevention is always desired over war, but it not always possible.

It is not the presence of military or the tactic of violence that makes war war. It is the purpose and nature of the conflict. The purpose and nature of COIN is that of civil emergency, and to address it as war typically makes it worse.
Violence is clearly one aspect that makes it a war, if there is no violence then it is something other than war.

This appears to be one of the great myths of the war; however, in fact most Vietnamese supported their government. The insurgents were NOT successful, they didn’t throw out the government in the end; conventional N. Vietnamese forces did. It would be helpful if people would get their history straight when using Vietnam as example, and not simply mimic the uninformed howls of the far left protesters.

What is the upside of taking over the role of COIN for the (equally illegitimate) government of Afghanistan and fighting their war for them?
Don’t see an upside at this time, but the missteps that led us from a punitive operation to destroy AQ in response to 9/11 to nation building are visible for all to see, and understandable when you leap without thinking it through first.

What would the downside be to having Afghans decide what the government of Afghanistan should be? Does anyone really believe that even if the Taliban did ultimately prevail there that they would be able to revert to their old ways of dark age Islam? Does anyone really believe that AQ trainees would be swinging on the monkey bars at training camps again, unmolested by Western CT capabilities?
If the Taliban were allowed to return within the first two to three years of our invasion there was no reason they wouldn’t return to their old ways; however, after fighting us for years now and learning much about how to compete for populace they probably wouldn’t revert to their original form of completely intolerant governance.

War is indeed politics. So is insurgency. But COIN is Governance and that is a very different thing indeed.
The character of the war is very different, so the strategy and tactics used to wage it must be different, but it is still warfare.