Alright, you've got me going, lol. Here are my thoughts on this, overall.
IMO, that emphasis is because of too much right brain, which is why both right and left are necessary to me. The problem is that some people focus so hard on their right brain that they only flip the problem, where it's all right and no left... which is what makes me wonder about these training methods- do they TRY to avoid the left brain, or is it natural, and so different from the normal left-brained thinking that they are more noticed than, let's say, training methods that use both?
Making a horse carry out a maneuver requires analytical thinking- praise the horse when he does well, discipline him when he does something bad. Give and take. My issue with this is that the ending for this is a horse that is a machine. Specified to one thing or the other. Logic says that this is what you want. On the flip side, the feelings, which associate with the right brain, make you not want to push the horse, not want to discipline him, let him get away with things to make him comfortable. As long as the horse is happy, it doesn't matter. The best trainers generally have some sort of a mix between right and left- because it's absolutely necessary. When a horse tries to bite you to get his grain, you don't let him do it to make him happy, which is what pure feeling would mean- you discipline him, which is a left-brain concept.
I'm not sure if I'm making sense, since these are just my garbled thoughts that I typed without correction... oh well

hope I didn't bore anyone.