Personally, I like lightweight hunting rifles and lightweight slings. I don't see the point in putting a heavy sling on a light rifle. Nylon webbing does the job for me just fine.
I also tend to carry my hunting rifles in my hands, not slung (which is the point of having light rifles), so it's pretty rare that I even have a sling on my rifle.
For elk season last year, I bought an Eberlestock Dragonfly pack with a rifle scabbard. It exceeded my expectations and that rifle scabbard is just handy as hell. I fell in love with it over the course of my 7 day elk hunt. No matter where I went, that pack was perfect. Usually I had my rifle in my hands, but if it was dark in the morning or back to camp, I'd throw the rifle in the scabbard and my hands were completely free. I hardly noticed the rifle in the pack. Best part was I could reach back there and pull the rifle out of the scabbard with one hand, in about 2 seconds. So I just left my sling in the truck after the 2nd day.
Honestly, if you haven't used a hunting pack with a rifle scabbard or a gun bearer system like the one Kifaru makes, you don't know what you're missing.
The idea of using a sling to steady your shooting is romantic, nostalgic and just fine on the battlefield, but for practical hunting shots, if you have time to use your sling, you have time to find a rest. For most western hunters, that's your pack. Take off your pack, throw it on the ground and shoot off your pack. Far better than standing with a sling. For eastern hunters, that's the nearest tree.