I'm asked this question at a few open shows per season. Currently most rule books do not permit bitless bridle.
At the Global Dressage Forum. Dr. Andrew McLean one of the panel experts “How you train the bitless bridle depends on the hands at the other end. I think you can have the horse light in anything.… It’s how you train it.”
When asked if a bitless bridle is kinder and more friendly to the horse, Dr. Hilary Clayton (one of the most respected researchers in equine mechanics and behaviour) replied, “I approach it scientifically. There is pressure on the nose. (With research technology) we looked at the cross-under bitless bridle and discovered there is twice as much pressure with this noseband, on a localized area. So padding the nosebands in that area is necessary. We need to look at more different types of bridles, but they are not totally benign either. It’s a matter of evaluating the horse. Don’t just assume you take the bit away and it’s more friendly.”