What's wrong with doing research on this subject? We should investigate as many possible causes of violence as we can, and let the facts take us where they may.
Interestingly, the gun lobby has pushed through laws that effectively ban the CDC from conducting a wide range of research into the causes of gun violence, and the links between gun ownership and crime rates. Those aren't the actions of people who are confident that their position (essentially that guns have absolutely nothing to do with crime) is true.
Anyway, the Supreme Court has already ruled that video games are a form of speech, and therefore covered by the First Amendment, so there's very little that the government could do to censor video games, or even restrict their sale, no matter what any research ultimately proves.
But if some conclusive link between violent media and violent behavior exists - which I doubt, but concede that it's possible - we should know. If nothing else, it would enable parents and retailers to make better decisions.