Strategy exists at all levels, what you're discussing IMO is little strategy, the strategy of how to "win" a particular operation or smaller scale war. COIN is unique, I know you don't consider it war and I do, but regardless we both understand it has a unique strategic context at the local level. Using the diplomacy, information, military, and economic (DIME) model, despite its limitations, all of these elements can perform at the tactical, operational, and strategic levels. In my opinion you're arguing we failed to understand the operational environment and had an ineffective operational approach. Certainly that is true, but we probably disagree on several points on what we did wrong.

Transitioning to big strategy, you have to look at the war in a global context, and that has little to with so called legitimacy at the local level. It had a much larger Cold War context. At this point in time it had everything to with relative power vis--vis the communist and so called free world. From that perspective the war demonstrated, that the U.S. was willing to stand up against perceived communist aggression. It demonstrated the U.S. was willing to support it allies, and as Lee said it gave time for the still weak governments in SE Asia to strengthen their defenses against USSR sponsored insurgencies. Over time it was realized, although I doubt it was an objective going in, that this war, much like our support to the resistance in Afghanistan helped weaken the USSR, which contributed to its collapse and our subsequent post-Cold War era where we often appear to be strategically adrift.

I disagree with that view, strategy is simply more complex in a multipolar or non-polar world, so it can't be explained in a Cold War context. Local issues still have global implications, but the implications vary greatly, and need to be considered on their own merits. The last thing we need is a strategy today that parallels our Cold War strategy. It would limit our options and more often than not cause us to mischaracterize issues.