Oh
Then it's not good for kids
It is not even for adults ;-)
For games it typcially adds nothing to the game play. There are cases where one can argue that it adds to realism, to set the style and atmosphere etc. Or even make the violence extra outlandish and unreal.
(Gore basically means blood. Lots of it. Not necessarily violence. A murder mystery with a big pool of dried blood would be gore without onscreen violence. And when I think about those Jason Bourne movies, there were some ultra violent close combat fighting scenes, but there was no gore.)
Life should be banned too, because it does have a lot of that stuff as well and has a negative impact on people ;-)
But seriously, for kids it is kinda banned. That is what those rating systems are for. And adults would have their mature content filtering (Steam has such, Itch not so much). But once you are legally an adult, "the" gov should have no business telling people what they can or cannot view, play or create. The thing is, what is frowned upon is different for every country. It is arbitrary and even changes with time. The US for example is rather strict on nudity and profanity (swearing), while violence seems ok. In Europe it is the other way around.
And for games, like in: fictional stuff, the discussion would have an additional layer of abstraction. Yeah, some non-players regularily claim that eg playing ego shooters makes people violent. They got it backward. Violent people might be interested in such games, but that is the same as having an interest in sport cars and playing racing games. I do not like to drive a kart, just because I played mario kart.
Some times Gore is good too, as it scares many people from actually commiting Gore. Before the advent of Gore games, there used to be many psycho killers and maniacs. Nowadays, maniacs and psychos plays brutal game games like PPG, mortal Kombat etc, Hence many psycho killers are gone. Everything has a reason. Government is no fool for not banning it.
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.
Uhm. That would be quite a corrupt country. If they acutally ban something, the reason for the ban does not cease to exist, just because the devs pay some ransom.
But maybe you are using the word ban differently than me. Adults Only for example is not a ban. And Steam delisting something is also not a ban, at least not a government ban. A government ban would be for something that is against the law. And only that. Because the gov is all about law. If it does not concern laws, the gov has no say in it. You have to break a law with the game. And that is very hard to do, if it is hand drawn. Stuff has been taken down for copyright issues. Or there is a famous example with some nudity of real life women, but the woman in question was 17 at the time of filming. They used real images in the game. If you do that, you have all the problems with that, including privacy issues. Some games could be classified as hate speech, or be meant to incite real actions that are illegal. If you make a game showing how to kill your teacher at your school, that is the kind of stuff that the gov would be interested in.
But banning for content you deem bad ... nah. That is censorship. And what is bad changes with time and place. In some arabic countries they really do ban games containing homosexuality, but tbf, I think that is illegal irl there too. wich would bring me back to the gta game example of depicting illegal acts in general. it is a game, not a manual or instruction to replicate this.
So protecting impressionable minors from the "bad influence" , all good. Protecting adults, nah, that is censorship. On itch you have to explicitly click a button to see adult stuff.
Psycho killers and maniacs used to be, but now play games instead? Seriously?
That is like claiming people stopped doing lewd stuff, but now play lewd games instead.
Admittedly, there is a rise and fall in statistics with serial killers, but I would not attribute that to games or lack thereof. The advancement in forensics allowed to identify murders as being serial murders in the first place. Not everything is as clear cut as Jack the Ripper cases. But that same advancements allowed to catch murderers before they became serial. Or even deter them or drive them to use methods that are again not detectable as serial cases.
If the gov would be really interested in effectifly reducing stuff like killing sprees by banning or not banning stuff, they should ban the news. No other thing inspires wannabe killers more.
If you want to hear a plausible idea, it may be due to leaded gasoline. Lead poisoning increases aggression. Leaded gasoline was introduced in the 1920s and banned around the 1990s.