A better analogy, bsms, would be Yoga. Learning yoga will not help you be a better ballet dancer, or cellist, or computer programmer. No, not directly....you have a better chance of being physically useful in your life if you do yoga. It is one of the very best foundational trainings a human can do.
Dressage is like yoga. It makes the hrose engage muscles on command that are needed to support the pelvis and back and keep the horse better prepared to carry the weight of the rider...
Here is where we disagree. I'd like to see evidence that yoga is "one of the very best foundational trainings a human can do". Oddly enough, lots of top athletes don't do yoga. Lots of folks who live long & healthy lives don't do yoga. One of my uncles did square dancing into his late 80s, but he didn't do yoga. An aunt lived healthy into her 90s, without doing yoga.
As some point, if yoga was truly "one of the very best foundational trainings a human can do", there would be some evidence for it. I'd be curious if there is any. I'd bet walking regularly has a better record of extending life and health than yoga does.
Dressage is the same way. There is no evidence that I've ever seen that a horse trained in dressage is healthier than a horse who is not. The studies that exist for how horses respond to carrying weight on their back would indicate, if anything, that dressage has nothing to do with it. A horse does not round its back to carry the weight. It may feel like that, because of other things the horse is doing, but the back itself does not lift, let alone round up. Effect of weight on the horse's back - Part 1
Shifting weight to the rear is something any horse will do if needed, with minimal practice, but it doesn't increase longevity, riding lifetime, etc.
If anyone has studies that show dressage increases the useful lifespan of a horse or make a horse healthier than a non-dressage horse, I'd love to see them.
I am not objecting to dressage. I enjoy watching dressage videos. I think both horse and rider are impressive. However, it is often oversold. Our understanding of how horses actually move and how they respond to loads is still primitive, but there are certainly indications that collection doesn't play a big role. When horses carry a heavier rider, they leave their feet on the ground longer:
"On a level surface the forelimbs consistently supported 57 percent of the forces while the hind limbs supported 43 percent. Going uphill, this pattern of distribution shifts, with 52 percent supported by the forelimbs while the hind limbs took on 48 percent. Time of contact also varied. At higher speeds, the two feet were on the ground about the same amount of time, but at slower speeds, the hind limbs tended to spend less time on the ground--an observation that had never been made before in quadrupeds, according to Wickler. For the front limbs, time of contact didn't change significantly whether on the level or on the incline, but the hind limbs tended to be in contact with the ground longer when going uphill...
...In short, explains Wickler, carrying a load causes a horse to shorten his stride, leave his feet on the ground longer and increase the distance his body travels (the "step length") with each stride. All of these gait adjustments work together to reduce the forces placed on the legs with each step." How Much Weight Can Your Horse Safely Carry?
Here is a discussion that rejects an idea I've read about in a variety of books:
"The thought that the lowering of the neck does increases the range of motion of the horse’s thoracolumbar spine is also inaccurate. " Stretching the Neck
This is another I found interesting:
"Simplicity is the greatest achievement of knowledge but simplicity without knowledge is the greatest cause of equine injuries. “The horse’s hind legs need to track up at working trot”,
is the type of simplistic formula which, if applied without sound understanding of the horse’s vertebral column mechanism and pelvis rotation, is likely to cause injury." Hind Legs Engagement and Stifle Problem
Again: I think dressage is an interesting sport, although all I ever do is watch it on YouTube. But I think it is oversold as a cross training event. Like yoga, I don't think there is evidence it is the best thing since sliced cheese. I could, however, see it as a great way to make a horse a more all-round performer.
I've noticed that jogging tightens muscles that need to stretch for riding, and riding seems to tighten muscles that stretch for jogging. I consider riding and jogging to be excellent ways of improving my overall health in complement to each other. But riding will not make me a faster runner, just as doing pushups don't help me run faster. They just makes me look slightly less like a dork, and help when I need to move around under our kitchen sink to replace a faucet...