I think it's ridiculous that still today this tradition is still here. If a rider is great then he won't need two bits in his horse's mouth to make wonderful things.
I understand that riders need to compete in the same condition, bu having a double bridle or a bit won't change that much, judges have to judge the horse and the rider not the equipment.
I think riders should be able to choose between a double bridle and a regular snaffle (it's the case in some countries at the national level). Of course, bits should be adapted to the horse anyway