When we constantly see death I do think there is a natural desensitization to it. I believe this is especially true the younger it starts. As a fully developed adult we can recognize a story, a movie, a game. We can fully differentiate between these things and the real world, but children aren't always able to do this on their own. I believe our kids are getting exposed to more and more violence at much younger ages and without strong parental influence, I do believe that it will desensitize them. Partner this desensitization with a significant mental illness and things can happen. Two of the most recent shooters had a fascination with the Joker from Batman.
Again, I do not think that this is the root of the problem, but I do think it is worth looking at. When I was a kid I remember having to ask my aunt for the 'gun' in order to play duck hunter on the Nintendo. She had made it inaccessible to make sure we didn't play with it and act like we were shooting each other. When my cousin and I played chess together we weren't allowed to 'kill' each other's pieces, we 'captured' them. At the same time I did watch violent movies when she wasn't around, and I played violent video games, and I even used sticks as guns and swords when playing with my cousin, but these extremes put on by my aunt helped me as a child to think about the severity of violence.
Ultimately, violence sells. Because of that we aren't going to be able to stop media violence unless it stops selling but I am not sure that we need to. I do think that we need to be aware of our children and what they are taking in. We should help our children process the violence that they see and help them recognize the difference between a game or a movie and real life. I believe there is a deeper root as to why violence is so attractive and why it effects our young people so much, but I do think it has an effect.