Granted non-skinned animal carcass will give you more materials. You can buy the Hunting Wagon & store a bunch of skins in there. Along with up to 5 large animals. I don't ride around with the Hunting Wagon. I just call the wagon throw the large animal or pelt in the wagon & dismiss it & go back to riding my horse to hunt. I use the wagon as a storage bin. This way I'm not riding back & forth to camp with only one large animal on my horse.
You can also skin medium animals too. Ofc the non-skinned medium animal will give you more, like 3+ materials compared to just a skin that will give you 1 material. But you can carry up to 30 skins of one type of medium animal in your satchel. So 30 rabbit skins, 30 raccoon skins, 30 snake skins & so on. So perfect medium animal skins might only give you 1 material, but if you collect 20 or so skins that is already 20+ materials for you Trader role. This also works for poor, good, & perfect too. Meaning 30 poor rabbit skins, 30 good rabbit skins & 30 perfect rabbit skins, that you can carry in your satchel. I think 30 is the max for each category.
Same thing with Birds (Vulture, Hawk, Eagle & Condors to name a few) I get 3 feather each time I skin these birds (If they are good or perfect) & can carry up to 30 feathers for each bird. Most feather will give you 0.90 material for each feather. If you collect 30 feathers that equals to 27.0 materials just for 30 Vulture feathers. Now you add in the other birds Hawk, Eagles, Condors at 27.0 each. That's a total of 108.0 materials for all 4 bird types. I just ride around shooting poor, good, perfect medium animals / birds & skin them. If I see a perfect large animal (Buck, Deer, Pronghorn, Bighorn Sheep, Cougar, Panther), I will kill it & toss the animal in the back of the hunting wagon. Then continue on my hunting trip. All of it adds up.