AnrewPL, I would agree that yanking on the reins or tearing the horse's face off with them is wrong. So would the US Cavalry. Military use included riding with a saber in your hand while fighting another guy who had a saber in HIS hand, and if you couldn't control your horse you died. And a cavalryman who spurred his horse bloody needed a good reason, or he'd face discipline from someone who liked horses enough to choose to spend his life with them. I have a horse who was spurred bloody when loaned to a ranch in Colorado, and he still has a 2" round scar on one side.
My main point on this thread is not to get anyone to ride in a chair seat, but to refute the idea that using a chair seat means you are incompetent, or that it will harm your horse. An extreme version was used by both the cavalry and a lot of cowboys. The cavalry rode their horses in a way almost no one does today. During the Civil War, they frequently would ride 30-50 miles/day for 3-5 days in a row, and then need to arrive ready for combat. And that wasn't on one horse, carefully trained for it, but 700-2000 horses and riders. Up at midnight, mounted by 1 AM, then moving out with a few thousand horses and riders in the darkness before Edison. With those numbers, below average riders would get teamed up with below average horses, yet everyone had to move in formation and arrive fit enough to fight.
If heels under hip improved their balance and made their horses fitter, they would have figured it out. They DID sent experienced people to Europe to learn about dressage, and even experimented with it. But their conclusion was that with average riders and average horses doing a lot of riding in rough country, dressage didn't fit. The horses broke down faster, and it took too much training for both man and horse. The cavalry needed for average men and average horses with minimal training to do impressive riding in all types of terrain and weather.
Cowboys in the west didn't work in arenas, and they were a long way from any medical help. They also were not highly trained riders using well trained horses - at least not until experience improved their ability. If putting their heels under their hip would improve their odds of staying alive, I think they would have done so.
That doesn't make it wrong to have heel under hip. It works very well - for some riding. And someone trained that way may well feel more comfortable riding that way all the time. That is fine, but a chair seat is not a fault for other riding needs. It is a different way of riding, and it has worked for a huge number of people and horses for many years. It takes a historical myopia to conclude that good riding was discovered in the 1960s or 70s, or that only wealthy Europeans rode well in the 1800s.
Personally, what seems to work best for me, is to normally ride with the rear of my heel in line with my belt buckle. It is easy to bring my heels back if I want a tight turn or a bit forward if I think my horse might balk.
A lot depends on the horse, the saddle and my goal for that day...all in the humble opinion of someone who doesn't compete, isn't a trainer or instructor or an anybody.