Almost everyone would react the way you describe-- the first time. But people are resilient. Expose them to enough atrocity, and if they survive, the horror of it will fade until it becomes a prosaic fact of life. We see it in soldiers. We see it in EMTs.

The coping mechanisms are not perfect. What we now call PTSD has and will continue to destroy lives long after the fighting is over. But they do allow for continued functioning in the field. For better or for worse.