Desensitization implies only that the natural reaction by any person with empathy to be shocked when faced with the endangerment or suffering another has been worn away.
When the sight of others' cruelty and others suffering incurs no reaction whatsoever you cease to understand and relate to other peoples' state of well-being.
I think you have a very different conception of what desensitization means than I do. I don't see it as meaning there is no reaction. I see it as meaning your mind no longer shuts down from shock or makes you feel ill or fly off into a bout of rage or grief that makes you do stupid things. The way I understand desensitization is when you've been exposed to something enough, you develop the ability to cope and maintain proper control of yourself, not that you completely cease to care.
Personally, I'm completely desensitized to gore. Only very specific kinds bother me, like parasites, eye damage, etc. I can see a picture of someone's head turned to spaghetti from a point-blank shotgun blast and not be really effected by it. This doesn't mean my empathy for the harmed person isn't exactly the same as if I wasn't desensitized. It just means I'm not emotionally traumatized and involuntarily toss up my stomach contents when confronted by it.
There are ways a person can become desensitized in a way that damages their empathy, such as repeated personal loss or betrayal causing someone to be less willing to invest emotionally in others. But that is completely different from being desensitized to violence, in my opinion.