The purpose of desensitizing a horse is not to teach them to react to nothing. It is to teach them to look to you for the appropriate response. It's to show them, that if you stay relaxed and calm; so should they. That is why when you start the process in ground work, you are supposed to keep your body language neutral and relaxed.
The purpose of sensitizing is to get them to respond to light pressure, like a change in your seat position, versus a heavy direct rein because that is what it takes to stop the horse on its best day..
The biggest issue with using desensitizing/sensitizing in training horses is finding the proper balance between the two. Wouldn't the world be perfect if it was 50-50 on every horse that you ever worked with? (I hope you can see the sarcasm dripping from that question.) Every horse, just like every human, is different and requires different ways of training. If you start with a horse that is laid back and quite frankly lazy, you will want to focus more on the sensitizing. Doing this will get the horse where it responds to your ques to move off your leg, or to simply move faster. If you were to start with a horse that is very reactive to everything, you would want to focus more on the desensitizing. This would help calm the horse down and probably slow it down. If you worked this horse on a 50-50 ratio, you would quickly turn it into a complete and total idiot that spooks at everything and bolts when you ask it to move off your leg. Whereas, if you done a 50-50 ratio with the laid back, lazy horse, it might not move at all for you, or it might have the energy and response of a fence post.
Neither desensitizing nor sensitizing is a complete training program by itself. They have to be used together and in balance for each particular horse for them to develop the proper results. This is what most people miss, and just to the desensitizing exercises. Find the balance for your horse, and you will end up with a horse that ignores what you want it to, but still responds lightly and quickly to your ques.
Good luck, happy trails, stay safe, and God bless you and yours.
Until next time,