Good speculation Gus, and a fruitful line of thinking. Haven't seen enough original pouches to say one way or another, but I have made bags from assorted leathers.
As you observe, elk is about as soft as deer, though thicker. Buffalo is firmer than elk, and thicker yet. That I've worked with has temper not as hard as veg tanned cow, however.
The pig I've worked with is the thinnest of all, and pretty fragile. Doesn't mean there aren't other weights, tempers and tans, but I'm not acquainted with them.
Lots of other leathers around back then too- horse, sheep, bear, dog, goat, even moose up north. Some common, some not, but available in places.
I guess the question is, if these were available to some degree and used for bags, would they have showed up among the bags surviving today?