Be as snarky as you want since your information is incorrect. I have seen grand prix dressage done in a snaffle, it is not allowed internationaly but it is allowed by BD.
Polo players don't do it for refinement they use harsh bits because their horses are not all that well schooled and are galloping in a group. They don't perticularly give a **** about whether they rip the horses mouth to shreds provided the horse turns. We have 15 polo ponies on the yard and I wouldnt subject any horse to the treatment that is apparently normal in polo.
Icant comment on barrel racers as it isnt a sport we have here however pc mounted games upto and including international level is done in snaffles.