Ascend,
It's not a "puff of wind", it's the bulk airflow over the blades. How does this puff of wind lift the helicopter off the ground?
The control input modifies the blade flight and airflow, and in a hugely amplified way, the lift is changed - you directed me right on that, so follow through.
It's a question of how the dynamics of the blades are changed, not that they are well-defined and that they change.
Precession and couples at 90 degrees are not the reason a rotor system behaves the way it does.
Then there is something special about a rotor system that makes it different from other objects in the rest of classical mechanics, unless by "precession and couples", you mean something different from angular momentum and forces. Summarize what it is, and I will believe you.
Helmet,
Stopping the elephant with your tongue would be equally illuminating if we concerned about linear momentum. If you were changing the flightpath of a fixed wing aircraft it would be important, and if you're barreling along in a helicopter it matters too. I disagree that it's a red herring.