A bird sits quietly until the moment it needs to take flight from a fox or other predator. Human hunting with guns has them staying still longer than they used to, because they're easy to bring down when they fly off. They're better off hoping the dog doesn't find them. They believe it is genetic.
Why wouldn't the same thing happen to deer, elk, etc., over time. The monster antlers already have a cost to them, but if they cause the animal to be specifically hunted for their racks, wouldn't those racks tend to become smaller over time, potentially even non-existent if antlerless bucks can hide among the females?