I believe that the original use was for incredibly light cues that not only cue at the bars, under the chin, and on the poll but also on the roof of the mouth. Just a design to give the horse one more thing to feel. You have to ride your horse with very soft hands in one of these because they can really cause a horse to gape their mouth if you take a hold of them even a little bit.
Also, I am not sure that horses have gag reflexes but considering a horses mouth is almost a foot long, I really don't think they need to worry about choking on it. LOL.