My recommendation is that the onus be clearly, and completely sat upon the lap of civil leadership. That it is the failures of civil government that allows the populace to move up the curve out of phase 0 "peace" into phase 1 "insurgency"; and that the role of the military is to bring in additional capacity to assist the civil govenrment establish a degree of security while the assess and address their inadequacies; and that once the military has helped get the populace back to the phase 0 box (a mix of reducing violence and improving governance required) its job is largely done.
Your logic isn't incorrect, but it is illogical based on the following context,

We're either there because we invaded (OIF and OEF-A), and that should never be confused with FID where we were invited in by the HN government, or we're there because the HN has invited us to help (often at our urging).

In the first case your arguments don't ring true, and in the second case we're there to help because we believe it is in our national interest, and at the same time we know the problem must be resolved politically, yet we normally know (even if we don't admit it) that the HN government isn't capable or willing to that. We're trying to sail a ship that won't float.

You asked where the military solution has worked, and I can name two places right off the top of my head where the military ruthlessly supressed an insurgency, Iraq and Syria. Probably a couple in Eastern Europe also. Where has the political situation worked?

when under our current legal constructs decisive effect can no longer be produced by the military. We stand with a foot in each camp, so to speak, in terms of how we understand and address these instances of popular discontent with governance within a state.
Is this a balanced approach, or simply dysfunctional?

Until civil governments embrace that a populace is like a yard
I don't disagree, but is our strategy to maintain the status quo until the government gets it? The problem with this strategy is we're defaulting to a dysfunctional entity to solve the problems we volunteered to take on.