To be perfectly fair, I don't necessarily think tie downs are always a substitution for bad training.
My opinion (as well as that of Ray Hunt, Tom Dorrance, Buck Brannaman, Dr. Deb Bennett, etc as far as what I have interpreted from their writings, instructional dvds and/or live at a clinic) is that a horse can make a faster, more athletic move if it is not braced against a tie-down. whether this is a rope horse, open jumper, polo pony, barrel horse, event horse, does not matter.
Now, if said horse has years and years of moving athletically, braced against a martingale or tie down, you can't just take off the device and get some magic fantastic performance. The horse has to develop his athletic turns, stops, jumps, etc without any devices. So a horse whose muscle memory and athletic patterns have developed with a device on, may very well be better off, if the device is left on. Retraining a horse to go without, is not simple or for the faint of heart.
Again, my undies are NOT in a bunch about folks trail riding a horse around in a loosely adjusted tie down, unless said horse will be asked to go through water crossings or up/down steep hills or through questionable footing.
My point is, there is a better way to do it, and it is NOT easy to find someone who can help you learn to do it, and there are excellent horsemen/olympic medalists/NFR finals winners who do not know how to help a horse go without AND perform up to 'world class' standards.
Buck Brannaman has not only played polo in a plain snaffle, but has re-trained 'ruined' polo ponies to play in a plain snaffle.
Yes, it can be done.
Too many people don't believe it, haven't seen it, may never believe it. I'm not going to save the world, here. I'm offering my opinion.
I wouldn't have believed it, unless I had both seen Buck, and had another of Ray Hunt's students help me get complete control of a spoiled OTTB in a plain snaffle, no noseband.