You want arbitrary censorship? By what standards? We are talking about banning stuff for adults. On what grounds? Restricting access to minors is all good and fine.
But if the activity is legal, why should a game or a movie be banned for adults? Swearing, gambling, drinking is all legal for adults.
And even for illegal activities, games and movies are not the real thing. Murder is illegal. So every crime series should be banned, because there is murder in it.
Know that Alien vs. Predator games? You can play as an Alien or Predator there, killing Humans.
Your wording is problematic. "your character just has to kill people for no reason". It is self contradictory. If the char "has" to do that, that implies a reason, but you state that there is no reason. So why "has" the char to do it?
For the USA, you basically cannot ban a game for its content, as it falls under free speech. There is that AO, Adults Only rating, but again, that falls under protection of minors. You will not find such a game in most stores, but that is not a ban.
Once you have the govs ban stuff, you will have countries ban games on grounds like "contains homosexuality". Or "has Winnie the Pooh in it" ( I kid you not). The "price" of freedom is to allow stuff (at least for adults), even if it violates your sense of morale, fashion, taste or whatever.