I don’t agree with you on that. Germany was not “defeated” in WWI and that led to the rise of Hitler. Germany was defeated decisively in WWII. Hearts and minds can come after you defeat an enemy not before. The same thing happens continually in the Balkans. Non-decisive endings lead to simmering tensions that eventually boil over into full blown warfare.
Another example is the Middle East. Every time Israel is about to defeat their enemies, the US and the West handcuff them and the Muslims are able to claim they weren’t defeated which eventually leads to another round of fighting.
Sure, we can use a divide and conquer strategy and we should. It worked for Caesar and it would work in Afganistan but you need to be the “strong horse” for them to follow since they will turn on a “weak horse”.
You are correct that Germany wasn't "defeated" in a conventional sense, they simply just went home, this did not lead to the rise of Hitler directly though, the punitive measures imposed by the treaty of Versailles (sp?) allowed conditions to become such that the rise of Hitler was enabled. If the Allies had let peace ensue, Hitler would not have had (legitimate) gripes to exploit among the people to allow him to gain power.
In a COIN strategy, the hearts and minds bit has to occur simultanously, while you still have the initiative and are able to control the situation, once you stop pressing forward against your opposition, if they still have the means to make war available to them, they will come back, as we've seen in Afghanistan. I'm not saying that going in hard down south again will give us utopia in Afghanistan, but it will take the fight out of them long enough for the government to come in and see to the needs of the people, win them over and continue operations against the hardline Taliban after we are gone.
That is victory for us.