If we were to ban games with too much violence, I don't believe we would be getting to the root of the problem. If the objective is to get rid of games with too much violence to make society safer as a whole then we should ban everything in the entertainment industry that's violent, not just games. Movies, music, and social media of all kinds should be included.
No, I do not believe games with too much violence should be banned. Games have a rating and only those that are old enough to purchase those games are able to do so. If parents decide to buy those game and allow their children to play them they should understand that the content is not appropriate for the age range. Furthermore, there has yet to be a ban on violent movies and almost every movie has some type of violence, even if it is comedic violence.