I understand what you are saying. The idea of western jumping does sound a bit odd to me, but western dressage I'm not so sure about. Having ridden both western, basic English hunt seat, and dressage, I feel that western is far more like dressage than English hunt seat. Western riding promotes a longer leg, riding primarily off the seat, turning away from the outside rein, the sitting trot, etc. Hunt seat (used in most other English style riding) promotes none of these, while dressage promotes them all.
But then alas, we come down to costume and tack. Outwardly they look different but western snaffles are certainly common and if you say that non-chairseat western saddles are also readily available, then it comes down to cosmetics and I'm not convinced that should be the deciding factor. After all, authentic cowboys didn't dress as your western riders of today, nor did the original inventors of the word "dressage" dress like dressage riders of today. A person in a western style community is not often inclined to switch over to English attire, nor should they have to IMO, just to ride dressage.
The answer of course, is for we who value what dressage has to offer the horse and rider, but don't care for the attire, to all join the "Baroque Equestrian Games and Institute" (I have) and compete under it's wonderful rules which allow any and all styles of tack and attire, while focusing only on the improvement of the horse and rider. (Beside strictly dressage classes, the BEGI also offers the artistic expression of musical and custume classes, as well as "games".)