Looks like cavalry, which often got in the habit of riding like that for a reason:
Taken in 1916. But a full load often looked more like this:
I think they got in the habit and then rode that way even if it wasn't needed. Much of how people ride is based on what they learn, and they then apply it even if it doesn't make sense in a different context. The very vertical position taught in dressage and WP is good for dressage & WP, but has too narrow a base of support for trail riding or riding green horses.
Riding like this is different:
It works well for some situations, and works particularly well in some western saddles - but it depends on having a very long leg. It shifts your weight forward, not back. It wraps your legs around the horse's center of gravity, which makes riding bucks easier (IMHO). It helps if your horse stumbles, since a stumble merely drives one down against your stirrups. It isn't how I choose to ride, but isn't all bad.
Maj Frank Tompkins, during a 28 day period, rode Kingfisher 580 miles thru the deserts and mountains of northern Mexico, on half rations most of the time. With gear and supplies, Kingfisher was carrying 220-250 lbs total - and Kingfisher weighed just under 800 lbs...so he was carrying 30% of his own weight. Tompkins wrote:
"In this drive he had but little grain, and that corn which he had never before eaten, no hay and what dead grass he could get during the night...He negotiated the snows of the mountain passes, he sweated through the noon-day heat of the lower levels, and he shivered at night from the icy winds of these high altitudes.
He never showed any signs of fatigue, never lost courage, and was a constant inspiration to his rider. He lost but little flesh, always moved with a quick springy step with head and tail alertly raised, animated and watchful. In battle he was fearless, being quite content to keep on the firing line without fuss or objection."
If the position was as bad as it looks, he would not have been able to load up an 800 lb stallion with 220-250 lbs of gear, ride him 581 miles in 28 days over some of the roughest terrain imaginable, and finish with "a quick springy step with head and tail alertly raised".