So far nobody's mentioned the tailplane.
Good point.
The book I mentioned also has pitch-coefficients vs AoA. The (typically nose down) pitching moment of the wing needs to be balanced by a tail-plane downforce, or some "standard" CoG position, in addition to any movable CoG issues.
But this down-force has to be balanced by extra lift at the wing, at high AoAs this leads to a lot of extra induced drag, and so it all goes on....
An aeroplane is a lot more than a wing.