It depends on if you need it or not.
You may need it for two reasons. One if your horse doesn't have a lot of muscles on its back and not much saddles fit it you will want to use a breast plat because the horse will be gaining muscles as you work it and the fit of your saddle may change and it may or may not start moving. And second if you have a martin gale you can choose to use the one attached to a breast plate instead of a traditional one because it fits more closely to the horse and there is lower probability that the horse's leg can get tangelled in it.
The con of a breast plate is that if it fits to tight it may proven your horse from pulling the neck down on jumps. A horse needs to be able to do so freely because otherwise it's hind legs drop faster and it will more likely nock a rail.
So in conclusion if you need one use one but be sure that it is not to tight (I like mine to have tight 4 fingers between the horse's neck and the strap), but if you don't need it don't use it because it looks nice because it may limit your horse's jumping potential.
Horses have a natural jump on their own. There’s a point where you can enhance technique. I don’t believe breastplates do that. I feel like some breastplates if fitted incorrectly can cause a ‘block’ In a horses jump and restricts shoulder movement but when fitted properly it’s mainly just an extra piece of tack to assist with the saddle not slipping back :)
I read the study and I don’t trust it. It was done by Fairfax who produced a breastplate which supposedly doesn’t affect a jump but that’s simply a tactic used to convince people to buy their product. It’s a biased statement.
More studies need to be done but not from sellers themselves.
Not to mention, there are multiple types of breastplates.
The training, tack, and individuality of the horse and rider need to be accounted for.