It doesn't cause less blood loss. The arrow may cause less blood to come out, I won't deny that, but a small diameter arrow will not plug or stop blood from coming out a 2" hole. No matter what scenario it is the same amount of blood loss in the animal.

Now using a small cutting diameter head, 1", has a much better chance of plugging up if the arrow stays in. I'm not saying this to bash small diameter heads but it is much higher probability of this happening with small heads. And yes I know you will say that smaller heads have a better chance of complete passthrough, but we're using the scenario of "if the arrow stays in" and there is no guarantee of a complete passthrough with any BH.