OP is also assuming a chest hit. What if your bullet impacts in the upper thigh or through the hips? In those instances I would want to be breaking bones, taking my opponents mobility from him.
In addition, an "instant stop" is usually the result of a debilitating hit to the central nervous system. This means a bullet that will reliably break the spine.
I get the feeling the OP hasn't done very much hunting....or at least he hasn't killed much game.