IGN has an extensive article that looks at the connection between playing games with violent content and real violence:

The psychology community is singular in its belief that playing violent videogames does have an effect on behavior, but it apparently is less of an effect than violent television imagery has. We can easily point to realism and exposure as the reason for this, but how much longer will it be true? Videogames become more realistic and more popular each year, so should we ban them now to prevent any adverse effects that children might have?

First amendment concerns aside, the issues come down to whether society is morally obligated to remove potentially harmful material from the children it is responsible for. If so, it seems there would have to be a ban on all violent media. According to Richard Gallagher, the literature shows that the impact of violent television is nearly twice as large as that of videogames. Removing violent videogames from youth's hands seems like it would have little impact on behavior.

Perhaps more effort should be spent to improve tried and true methods, such as parental involvement. You'd be hard pressed to find a single argument against parents having more participation in their children's lives and the research backs this up with positive results. Remember the study that looked at trait hostility and violent games? One other finding was that when children reported parental involvement in their videogame playing and game choices, they also reported improved grades and less aggressive behaviors.