Here we have the issue when a question is much more terrifying than the answer. I would start with the following statement to make it all clear. Yes, violence in media may be bad for kids, no doubts. Sometimes it leads to the consequences of aggressive behavior, commencing crimes, etc. Still, if we look at the question from a slightly different perspective, we might notice, that under a proper and wise parental control, violence in media may have a positive influence on child's development, and here is why.
There is a quite famous saying from Melanie Moore. She is a writer, holds a Ph.D. in psychology, and works with urban teenagers. So she said: “Fear, greed, power-hunger, rage: these are aspects of our selves that we try not to experience in our lives but often want, even need, to experience vicariously through stories of others. Children need violent entertainment to explore the inescapable feelings that they’ve been taught to deny, and to reintegrate those feelings into a more whole, more complex, more resilient selfhood.”
Every child, no matter how happy in daily life, feels rage. We cannot deny this fact. It is an emotion, and people experience emotions. Children too. And if they don’t have a place where they can throw it away, then we come to psychological problems with the vast variety of possible consequences. So this is where violent media can be good for kids. It can become a perfect tool for children to master their rage and anger. It all can be combined under the name “creative violence.” All the head-bonking cartoons, bloody video games, playground karate, toy guns, movies and TV Shows, all of them can serve as an excellent platform to transform negative emotions into creativeness and thus get rid of them, along with creating something new. No harm benefits only.
The world is terrifying, for being unpredictable and uncontrollable. Being angry because of that is a normal reaction. Still, rage usually paralyzes people. They stuck in feeling it and not knowing what to do with it. Transforming it into creativity sounds not that bad, right? And violence in media can help children learn how to do that.