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That's why the best course of action is to not censor at all and allow the system to work itself out.
I should clarify, I'm not advocating complete freedom in this regard. We don't want a society where it's hard to be a gay person because lots of companies deny service to homosexuals. However, we also can't claim that every company should always have to serve everyone. There is certainly some nuance and ambiguity here, but not hosting services for groups which support far-right terror seems to be fairly reasonable.
In the 1700's, when we were having the debate over speech protected from government interference, someone could have easily said "yes well if you don't like the government's policies you should go to another country!"
The existence of alternatives is irrelevant to the fact that freedom of speech is sacred and forums for speech - public or private - must never infringe upon its freedom.
If you study our jurisprudence you’ll find that no free speech cases were decided by the Supreme Court despite plenty of common law surrounding speech such as civil libel, commercial regulations, etc. for nearly 150 years (!) until the early 1900s. Debs v U.S. (1919) was the first case and it was about - surprise, surprise - an anti-war speech.
I don't think it's that simple. Taken at face value, you want it to be illegal for someone (say, a game publisher) to have a discussion forum which facilities speech around a particular topic (say, their game) while banning off-topic discussions (say, porn). I'm therefore going to assume you're just thinking of companies which facilitate all kinds of speech, such as forums like Reddit and Twitter and infrastructure like Cloudflare, but excluding Hacker News and lobste.rs and /r/factorio which focus on a particular subject area.
The problem with your approach is that, invariably, a discussion forum which doesn't get rid of despicable content ends up repelling people who dislike that content and attracting people who like that kind of content. A great example is voat.co, which looked like a fairly good Reddit alternative until its free speech absolutism ended up attracting all kinds of hateful people and content.
If a platform isn't allowed to reject legal speech, we would need much stronger laws regarding what counts as hate speech and what doesn't. I don't know if that's what you want.
In this case, the idea is to lose a bit of free speech, and gain less hatred and less murder. That is not an arbitrary judgement; admittedly this is also not a clear-cut judgement.
The system never works itself out, successful societies are the ones which have established governing rules. Game theory has given us pretty good indication that systems rather self-destruct without governance than self-stabilize.
I disagree with this sentiment, and upon reflection of why, it seems we've come to a real-life example of the trolly problem. Choosing to be passive and "let the system sort itself out" will almost certainly result in more deaths (edit: specifically in terms of mass shootings), but choosing to be active means the powers that be are forced to make subjective choices. I personally believe that it's worth taking on the responsibility of subjective choice.
Edit: However, I also realize that censorship oftentimes just ostracizes already-radical groups. This has the advantage of making it harder for them to find an audience, but also allows them to radicalize further while under less scrutiny, which also seems like a complicated balance to me.
what if rather than being a viper pit of nefarious hatemongers seeking to brainwash the youth into committing acts of violence, imageboards tend to be popular among a subset of the population more prone to depression & more severe mental illnesses which also happens to the encompass the the kinds of loser psychopath edgelords who commit these sorts of crimes. the whole response around these events simply shows we've learned nothing from columbine and are still in essence trying to eradicate the trenchcoat mafia.
Sure, 8ch is also full of autists who just need a hug (subject to certain terms and conditions) but if I discover that a bunch of people are making plans to kill me I'm not under any obligation to put my enemy's problems ahead of my own survival.
