It also allows for different communication. A leverage bit acts differently than a snaffle. So with a double bridle you can truly use the two methods independently. Its also why a pelham should be used with 2 reins, you just then have 1 mouthpiece instead of two, so not quite as refined.
Vix, a double bridle does consist of 2 bits, a small snaffle like bit called a bridoon, and bit with shanks called a weymouth. It is used on highly trained horses and should only be used by highly skilled riders.
The historical use is that it helps give very detailed and sensitive aids while riding to help in upper level movements. Can those be done in a snaffle, yes, if horse is properly trained. Why the double bridle then? My guess nowadays is because way back when it was considered more *formal* - and hence why rule changes allow the choice between a double bridle or not.
But just because it is a double does not make it bad
thats only my opinion and like i had said, it wasn't 100% correct to everyone and nobody has to agree with it, im not hating on the people who decide to use one.