The Double Bridle can lead to a beautiful conversation
In modern dressage, the double bridle is often used as if both bits were designed identically. Most riders hold all four reins with the same tension. So the horse and rider don't get the benefit of the finesse of two bits that are designed differently and act very differently. The double bridle is not intended as a part of a costume. It is not there to get the head down. It is not there as brakes to stop your horse! In reality, the double bridle can bring a whole new dimension to the conversation with your horse.
For me, introducing the double bridle is almost like being slightly near-sighted and putting on glasses. With glasses, I can see a lot better. With a double bridle, you can feel a lot more details because you receive information through four reins and two different channels. And you can talk to the horse even more precisely than with just a snaffle.