Yes, to start off, I will be the first to say that I do use many training techniques that would be classified "NH", however, I find that many NH trainers over-emphasize their reliance on some of these techniques. All of my horses need to know how to give to pressure, but I personally believe that there is such thing as a horse that is too light to pressure.
For example "give to the bit", I do not want a horse to brace against the bit and hang on my hands, but I also do not one so soft that they drop their head away from the slightest pressure. Why? When the horse drops the chin directly to the neck, they are "arching", but they are not lifting the back, lifting through c6 and c7, and stretching the cervical vertebrae. They still end up pulling largely through the lower muscles in their neck as they have never actually learned to engage the hind end, use their abdominals, and lift the back.
Next, disengaging the hind end..... Yes, all horses do need to know how to do it, but rotating the hip joint without proper flexion can be damaging. The axial rotation in the hip joint is limited. I have seen a very common posture with horses that are asked to do this repetitively, something that many NH trainers encourage. Working with horses with this, actually teaching them to truly "engage" is pretty challenging. When the hind end isn't working properly, it transfers through the rest of the body. I have seen many with joint issues, back issues, etc.
I have also seen many of these horses achieve obedience at the expense of their bodies, learning how to give to pressure despite the obvious conflict with the correct function of their body.
Again, I do think that these techniques are necessary for horses to learn, granted that they aren't overdone. Overdoing anything is harmful, but I find that many people find comfort in these exercises because they are easily accomplished. I am personally not a huge fan of any particular clinician, I have never actually managed to watch a whole show or DVD. I would actually lean towards Buck, Hunt, or Dorrance to actually learn the techniques. I would then start working more with the body, always keeping the mind in check, but spending more time on physical correctness. Too much obedience in a horse can hinder that horse's ability to really let you know when something isn't working right. I work through the relationship for honesty, respect, and a mutual understanding, not only that "if I do this, and you do that, I will release pressure", but working as the horses personal trainer, working through the mind and the body to read where any imbalance is occuring.