Jake: Stickbows are only as accurate as the folks shooting them, and most shooters aren't very accurate. I agree that shooting at longer ranges helps improve accuracy on shorter shots as well.
I limit my long range shots for a couple of other reasons. First, if the animal moves just a little from the time the arrow leaves the bow until it hits the animal, it can turn what was an accurate shot into a gut shot, or other low percentage shot. Second, at 40 yards, in any kind of cover, I can't see small brush, sticks, etc., near the critter that might deflect an arrow making it a bad shot. Third, I feel a whole lot better about positioning myself at 10-15 yards from the critter, particularly a mature critter of the species, than I do about a 30-40-yard kill shot.