How is that changing my position.
Because you said you can change airspeed with power alone.
Doesn't both changes to pitch and to power affect the AOA?
Let's not use "pitch" here, because pitch is the result of an AOA or thrust change and not causal itself. E.g., pushing on the yoke in slow flight may result in a *higher* pitch attitude eventually, because the drag reduction may enable the aircraft to climb.
Thrust *can* affect your AOA if the thrust line does not go through the CG. If the thrustline is above the CG, then advancing the throttle can produce an airspeed increase. If the thrustline is below the CG, then thrust can produce an airspeed decrease. These are secondary effects and there are others, but they are specific to particular airplanes. For a generic analysis, you assume that the thrustline is in line with the CG. In this case, thrust will not affect the AOA.
Then I don't understand why our method is wrong to you.
I detailed the problems with your model above, nicely numbered, so I won't repeat them. Your method works during
normal flight regimes, but for reasons that differ from what you said.
99% of pilots out there do not need to understand aerodynamics as well as you do to safely fly a plane and the 1% that do will learn it.
There are a lot of student pilots out there who know you fix airspeed problems by
pushing on the yoke, so it obviously doesn't take an aerodynamics degree. If you get very low and very slow on final in an aircraft with limited amounts of thrust, that's the only thing that's going to save you.
You've got to push down in order to go up. The pitching for altitude model just won't cut it, even ignoring the possibility of a stall.