Jay’s point notwithstanding, here’s my take:
it’s about putting your center of gravity over the horse’s center of gravity. From there, the theory goes, you are easier to carry. And in addition to theory, my experience suggests that riding closer to the center of gravity makes my signals be more about subtle shifts in weight. That is to say, I can speak to the horse more with balance rather than leg or hand.
I learned about this while shopping for my first dressage saddle since the County Competitor I owned in high school. I assumed I wanted a deep bucket. But some ladies at my barn were all about those Stubben Tristan Specials made famous by Catherine Haddad.
Those saddles involved a different way of riding. You had to get core strength, relaxed hips and balance because their was no appreciable saddle bits to help stop the forward and backward motion of your pelvis. As these Stubben Pimps put it: “You can develop the core and relaxed, flexible hips you need for dressage now, with this saddle, or you can delay that for a decade by starting out in a saddle that seems to do that muscular work for you.”
Being old, and having been re-taught to ride correctly in a Prix Des Nations after a foundational childhood spent in badly balanced, deep lesson-horse saddles, I picked the harder, shorter route-- the Stubben Tristan Special.
And specifically to your point: This saddle let me ride tall, the front of my body open (and so my core was engaged) and right up close to the withers. And from there, the horse I was riding went really differently, from the very.first.ride.
First of all, my aids were quite “loud” to him. I think that meant he could feel the effects of my balance (or lack of that) much better when I was up close to his withers.
And second, when we figured out our new feel, this horse lifted up his front end in a way that I didn’t think he could have done.
So, in sum, I discovered that a forward balanced, minimalist saddle helped purify my riding.
Also, I it’s easier to sit when we’re close to the withers and closer to the horse’s center of gravity (which will still be ahead of ours, at least for most of the horse’s training.) So I reasoned that buying the saddle with big blocks that put me well back behind the withers actually made the gaits harder to sit… but disguised the problem with that deep seat and big blocks.
Take what you like and leave the rest. I think everyone just needs to try out different saddles… when the shape or design is really different, you really might need to give it two or three rides. The first ride almost always feels catastrophically wrong… especially if you aren’t relaxed in the hips. Stiff legs will make any new saddle design feel bad… you’ll just bump into its parts. So trying saddles might need to include a conscious effort to relax all the joints in your legs and “just follow” the horse’s motion for that first ride.