The dressage saddle is distinguished from other English saddles by two features in particular, the first being a very deep riding seat and the second a long, straight cut flap. The deep seat allows the rider to feel more secure during the many changes of position required in dressage performance, leaving the rider free to focus on guiding the horse instead of fighting to remain seated. The longer flap allows the rider to stretch out their legs, instead of keeping them high and tight as do competitive jumpers. Both these features are intended to keep the rider focused on the matter of making the gentle, almost invisible motions required to steer the horse through a proper dressage routine, giving them much more control than a jumping or general purpose saddle.
There is definitely a case to be made for using a synthetic dressage saddle over a leather version, specifically relating to the weight. The weight savings of a synthetic saddle allows a rider to execute commands to the horse for less pressure than the denser leather saddle would require, as well as making less demand on the horse’s endurance in competitions. In addition, there is the practical consideration of reduced initial and maintaining costs for synthetic saddles, and less time spent maintaining is more time spent caring for the horse itself, and more time out riding.