Properly done, desensitizing is NOT making a laundry list of things the horse doesn't care about any more. It is about teaching the horse A) fear does not equal run, and B) if your rider says it is OK, it is OK. A tarp isn't magic. Some horses are afraid of it, so it becomes something that causes fear, so the horse can learn that "A) fear does not equal run, and B) if your rider says it is OK, it is OK". Lots of other things can be used, but it is about building confidence in the horse that the RIDER knows what is scary or not.
Doing it right, you don't freak the horse out. A freaked out horse isn't learning anything. You use it - the scary thing - to build tension, and let the horse learn that if you are calm, he can be calm too. If you push it too far, so the horse freaks, then all he learns is that his rider likes to torment him, and you've just gone 50 steps backwards. And too many people time the release badly, or push the horse until he blows, and then they don't know why their horse won't trust them.
There are cases where true desensitization is needed. A few months while loaned to a ranch in Colorado taught Trooper to be terrified of lariats and men in cowboy hats (women in cowboy hats worried him, but not like men did). As in, "break thru the corral panels in panic" terrified. I guess spurring 2" holes into the horse's side will do that. So one of the things he needed was to learn that there was nothing scary about lariats and cowboy hats. I hired a pro to work him 5 days a week, and it took 4 weeks to desensitize him to lariats and cowboy hats. But once he was, he quickly turned into the only horse I've got that I trust completely. Trooper was a ranch horse, and the ranch he was raised on raised him well. 3 months on loan screwed with his mind so much that it took 8 months of rest, followed by 5 weeks of full time training, followed by about 6 months on the "You can do no wrong" program to get him back to where he had been.
Most horses never need true desensitization. Most benefit from good "desensitization", which would probably be better called "trust building". Maybe then people would understand the object isn't to scare your horse senseless...
Trooper a few weeks after arriving at our place. You can see the hole itself has healed over, but even now there is a 1-2" spot of lumpy bald flesh where he was spurred. The wither pressure marks are still there too:
After a lot of work retraining him - kudos to the pro, because I didn't have the skill: