Volume
I don't agree with your disagreement.
Lift coefficient at very high angles of attack is very high, and in the stall, even well inside it, it is very high too, compared with typical cruise angle of attack.
Of course, if you keep pulling and pulling and your aoa increases a lot, then even CL will be low. We agree in that. But even in that case, if you have enough power and means to maintain a given attitude steadily, you can fly the airplane. However this is extremely difficult, specially the control part.
So if pilots were indoctrinated in this, maybe using modern fighter jets as an example, they could be convinced than pushing the stick is the right thing to do whenever they face a stall or impending stall situation.
In my flight school, long time ago, in the piper arrow we practiced a manoeuvre called something like "characteristic stall", which was a progressive stalling of the airplane in landing configuration. The exercise was successful if after the stall warning you recovered the stall... without losing more than 20 ft. Many times this exercise was carried out at merely 500 ft, over the runway!
I had lots of arguments for that with instructors, but I only had about 120 hours. Now I know I was right. The whole industry met only to clarify my point.
Negative training is intensive and extensive and it is everywhere. One day they should address it seriously, it deserves more attention.