I don't entirely disagree.
I understand what your definition is saying however, the most important angle we talk about is the angle of attack of the wing. That's the one that'll kill you and that's the one that we need to stay flying.
We need to change the angle of attack of the wing to maintain or change the amount of lift that we require. The AoA of the aircraft is only relevant because it's attached to the wing and changing one will change the other. Untill you involve the slats and flaps.
You could probably design an aircraft which would fly around with an aircraft AoA of 90 degrees whilst the wing AoA remained within the safe and usable limits that it is intended to. I grant you it would look rather odd though!