yet it needs to discredit the aerodynamic explanation in order to sound plausible.
There is absolutely no incompatibility.
Do you analyze some problems using forces and some by considering energy? Both are appropriate, and compatible, but in some cases one might be more useful than the other. Look at a roller coaster as an example: how best to decide how tough the track needs to be at a point? - watch instantaneous accelerations. How to picture how the whole thing works? - watch the conversion of energy.
I fail to understand the theological nature of the passions. Angular momentum exists and changes in the way that it does. Why fight it?
Could it just be the hours and hours invested in being able to answer quiz questions about all the flapping, flying and phases? It still strikes me as a tutorial artifice developed to avoid having to address the issue of angular momentum in class.
Every pilot in the British military, and a whole lot more across the world, are taught the aerodynamic explanation and understand it completely.
Well, it appears that some wacky ideas about systems with lots of angular momentum still persist despite this complete understanding - for example the questions about slope landings and the consequences of a gentle push.
If you're happy with that explanation, fine. But, if nothing else, keeping the direction of the change in angular momentum will help to keep track of all the phase terms.