I was under the impression that it's also a way to communicate in a more complex way with the horse, as in dressage. Is that also correct? I ride western lol so I only know so much on the subject.
The double bridle gives you an added means of communication, once the horse reaches a level of education that an extra means of communication will be useful.
99% of the time the curb rein will not be engaged, but when performing a highly collected movement, such as the canter pirouette, a touch of the curb can help to keep the horse contained enough to successfully complete the movement.
If you are needing to use the curb as a brake, you need to go back and rework your basic training with the horse.