I'm going to go against the grain here on this one (based on the responses).
I personally don't like tie downs either. I would like the horse to learn to balance on their own. None of my horses learn the barrels or any gaming event with a tie down.
HOWEVER ..... there is a time and a place for tie downs in barrel racing. There are some horses that just plain run better with a tie down. It's not that they aren't balanced in the first place, but they'll run better with one.
So when I have a horse that is already going well on the pattern, I will try a tie down and see what happens. If it seems to help them, I'll keep it on. If it doesn't seem to make a difference, then they don't wear one.
A tie down is like any other piece of tack. It should never be used to mask a problem (ex: force the head lower, or provide balance to a horse because the horse doesn't have any on their own), but it certainly has it's place and can be useful when used correctly.