BSMS, balanced seat riding is nothing new. My pictures are hundreds of years older than yours are. They, CLEARLY show a rider not sitting in a lounge chair with their legs thrust in front of them...
The big difference is not what is "proper" it is more about what you are doing at the time. Cowboys and cavalry riders were spending LONG hours in the saddle. No one will deny that it is easier on the human (especially male) anatomy to sit in a chair seat. It takes a lot of pressure off of out tenderer parts. So, it is easier on us, but NOT easier on our horses. Chair seats is very hard on them...
Even old paintings of how cowboys SHOULD look are not chair seats
The same with how the cavalry felt they SHOULD look....not how they survived 12 hours in the saddle
As drawn by an artist there at the time.
Actually, most of those pictures do NOT show someone with shoulder - hip - heel alignment. If a vertical line goes from the back of the heel to the belt buckle, or further forward, you do NOT have shoulder - hip - heel alignment - do you...
That is true going back to the Greeks, actually.
Here is the photo NBEventer praised:
The back of the heel is at the belt buckle, not under the hip. And that is on a slow moving horse in an arena.
Again, riding is about motion. If your hips move WITH the horse, then your hips won't HINDER your horse. And since a western saddle tree extends much further back than an English one, it makes sense to carry more weight aft in a western seat. That is, after all, how the western saddle is designed.
What would be wrong in an English saddle may well be fine in a western one, BECAUSE THE SADDLES DIFFER!
And if you want to discuss "proper western riding", then it is entirely reasonable to look at how westerners rode when it was normal to ride hundreds of miles each week. But you also need to understand HOW they rode - with a loose, flexible back moving WITH the horse. That style didn't involve posting.
If they could ride 200+ miles in a week, and finish a 40 mile ride by riding into a battle where their life depending on their horse, then MAYBE it works.
In any case, if your pictures do not show a shoulder - hip - heel alignment, then they support my argument.
Here are some more:
From the 800s:
A 1635 canvas:
From École de Cavalerie by Francois Robichon de la Guérinière 1729:
From Dupaty de Clam in the late 1700s (le Trot):
You get the idea. And the cavalry taught the back of the heel should be an inch in front of the chest.
Heck, look at the WP picture posted earlier, with an accurate vertical line drawn - the US Cavalry wouldn't have objected too much:
Not as far forward as the old cowboys, but she isn't riding a green horse in work that requires fast and unpredictable stops.
Lets see if I can explain WHY it works OK.
In the picture below, I added some lines.
The red and blue lines show when the body is bent, feet forward. The black line is exaggerated, but show the body as it would be if the hips move with the arrow into a straight line. By moving like that, the hips can move with the horse in motion, and thus are not putting pressure on the horse and saddle.
When vertical, the spine cannot compress. You have to post to relieve the horse's back, because the back cannot lift without lifting a vertical object that then comes down - and into the horse's back.
By having a body fold, and then unfolding it to follow the movement of the horse's back, even someone stiff like me can move with the horse, because the hinge of the hip allows for the motion. Done properly, the entire saddle can lift with the back. And since a western saddle distributes weight over a larger area and well behind the cantle, the effect allows a free and protected back by the horse.
Admittedly, if you put weight into forward stirrups, and then just bounce your body up and down, pivoting around the stirrups, hips rigid, you WILL beat the horse's back.
One of the things I love about Littauer is his emphasis on motion - that no position is right when looked at static. I can ride with my body having shoulder - hip - heel aligned vertically, and beat my horse's back. I know, because I've done it. Some riders can ride that way without beating the horse. And many post because in that position it is hard NOT to beat the horse at a trot.
Riding in the style of the old cowboys, which is a legitimate version of western riding, you can allow the stirrup to be a pivot point, and use your body like a jackhammer. Or you can flex, as I attempted to draw and as I believe Craig Cameron shows in video. And if you flex right, you will be using the saddle in the way it was designed, AND putting very little pressure on the horse's back.
You can be a pee-poor rider either way. And yes, I've been a pee-poor rider BOTH ways. But I've also learned somewhat how to do it right with feet well forward, and also learned with some limitations how to do it with my heels under my hip:
Unlike most of those posting, I've TRIED both, and if my horses are correct, BOTH can work. Heck, I normally prefer a somewhat *******ized version of a forward seat, and it works too!
That is my point, and I'm puzzled that it seem controversial - there is more than one effective way to ride a horse.