One: there is no link between violent video games and violent behavior, period. There has NEVER been a study that has shown causation or even a correlation between the two.
Two: video games are an art. Becuase of this, they are ABSOLUTELY protected by the first amendment, and can't be banned to anyone.
Three: it is not the job of the government to protect kids. It is the job of the PARENTS to understand the rating systems and make INTELLIGENT DECISIONS. The ESRB is a great system of self regulation (that darn free market working again), and provides all of the information the parents need.
Four: if minors want video games, banned or not, they will get them. This argument also applies to porn, gambling, drugs, rated R movies, etc.
There you go. You can't just regulate everything you don't like.