Now that's an American "brush" deer hunter talking there? Someone who shoots standing up as his quarry walks past. I think? And that's interesting as yes I can't disagree. I had never thought about it Southern until you posted this. Yet on the classic "Brit" stalking rifle the grip is much more open. Because I'm suggesting as we by custom shot our deer whilst lying on our bellies for us an open grip works better. I had never thought of that. That's very to the point Southern and does explain a lot about the closed grips on your USA "custom" makers of American market hunting rifles as against more open grips on bespoke "Brit" rifles made for the UK market. And why all those P-Hale rifles made for the USA market, but also sold here, always seemed to have a grip curve like a horse's hoof!
I was thinking more of deer drives, in the South, where deer and boar are pushed out of thick woods towards stand hunters. Large tracks of timber for logging in very flat Low Country land will be divided by logging roads into blocks, 1/4 mile on each side. A single driver with something like a Browning A5 12 gauge loaded with 00 Buckshot will slowly work with disciplined hounds, pushing, not chasing, deer and boar to move across these roads.
Hunters will be posted 100 yards apart, with shotguns, and narrow lanes of safe fire.
Think also of a boar hunter on a high stand in Germany, looking down a road, where wild pigs are being pushed down their trails, running across that road. He has to make a longs swing, picking them up with his iron sights or red-dot sight on a rifle, and be on for the shot as his chosen target leaps into the clearing, squeeze the trigger, and follow through. He might be better served by a more closed grip and higher comb with more weight forward, like a sporting clays or trap shooter would prefer.
The still hunter in big open woods will move very slowly, alone or with a companion, taking turns moving and mostly stopping to look. The shot they get will be more like flushed pheasant, going away at an angle. No much swinging; more like pointing out ahead of the moving target and mounting the rifle and firing almost subconsciously, as the sight locks on "the spot". A straight stock lever action or a more traditional rifle of the 1930s - American, German, or British - with open grip and thin fore end putting your lead hand close to the barrel, is fast, like a Churchill XXV.