Agree with a lot you said there SF, especially the part about off hand shooting. But then again that's why very very few hunters shoot off hand at game beyond point blank. Improvised rests like fences, trees, truck hoods, etc or "carry along" rests like bipods, shooting sticks and backpacks are what most hunters use once range get out there very far. Does that wring as much accuracy outta their guns as a good solid bench and rest at the range? Nope. But it makes 200-300 yards shots at game with commercial sporters doable where as you'd be hitting dirt 1/2 the time or more with your 3-4 moa surplus guns.
Is accuracy everything? Well it certainly never hurt.