I agree that the bending to your stirrup a lot is not productive, IMO. If the horse cannot bend around without twisting /rotating his head, then you are not . really getting the kind of softening and stretching that you want. you get a lot of rotation in the neck, but the poll does not "let go" of it's tightness, if that is a problem. The horse "breaks" behind the poll, so, in effect, avoids the flexion of the poll joint, which is so beneficial to him. and is integreal to him correctly ridden dressage.
It's not how far he can reach, it's the quality of the bend and stretch.
My personal impression is that CA approaches horses with a very adversarial point of view . it is personally distasteful to me, and though it might get results, I think it can make a horse operate more out of force and fear than from a willingness to try. it's very hard for me to explain or bring up clear examples of why I would say this. If you watch how he worked with colts at the Road to the Horse, and compare that to how Chris Cox worked, you can palpably feel the hardness in CA, compared to the firmness in Cox. There is a difference.