I use draw reins but only when I feel the need to. (As in not all the time) I think if used properly, there are no more harmful than a bit, crop, saddle, martingale, etc. can and/or should be. Bits don't ruin horse's mouths, rough hands do. Draw reins don't force a horse to do anything that regular reins can't effectively do, its just a little added leverage. I used draw reins when I was training for Western Pleasure.. I used to ride my horse in an English snaffle and warm up using my draw reins and regular snaffle rein. I use the draw rein like a curb rein- only when needed. So when my horse started to lose his headset a bit, I'd use the draw rein.. When he set his head correctly, I relieved the pressure.
Effectively, its no different than using regular reins it just provides a little stronger leverage. As far as natural horsemanship is concerned, I'm not against it persay.. but any type of tack or even human contact isn't "natural" so if you are saying not to use draw reins because they are "unnatural" then why not rid yourself of all tack.
I think another advantage to them, is a horse whose neck is a little stiff or the muscle is underdeveloped, it helps provide a little muscle memory. (If this is the case, then you really shouldn't overdo it, because you don't want it to be a negative experience or to strain the muscles, etc.) Just using them 10 or so minutes a day can help loosen up a stiff horse, and make the rest of the ride less of a struggle.