Twitch is basically the NBA of their streaming platform, as in they set rules for how streamers, viewers, and moderators interact. Twitch can create whatever arbitrary rules it wants to maximize their revenue. If advertisers stopped caring about controversy, or if Twitch suddenly found a better revenue source, they would surely pursue it.
I'll tentatively assume you got some of the same visceral recoil I got from that mental image. And that we agree that following everything Hollywood does is probably not for the best. So I'll ask you: if you could solve this however you'd like (by passing laws, let's say), how would you do it?
Passing laws to address this might work, but I think it would be difficult, and I would expect them to be challenged mercilessly. In order to actually work, I think this would require "Civil Rights Act" or "Equal Employment Opportunity Act" caliber landmark legislation, and I'm skeptical that this would be politically tenable any time soon.
The terms of service are not in anyway enforced consistently or fairly. The way the terms and service is written is that they can basically boot you for any reason. It is well known that the "tiddie streamers" regularly get away with ToS violations, where some dude wearing a red hat will get a ban (and I mean a red hat, because that exactly what happened to one guy, he didn't even have a MAGA hat).
"Behaviour off platform" can mean anything and will be like the current Terms of Service be not be enforced in any manner that is consistent or fair.
Twitch is a monopoly in this space and it is abusing its position. This combined with the fact that the mobile phone platforms can remove an App for any reason it wants means that there is no open market where a competitor that has a different ToS can reasonably become competitive.
> are incredibly few esports careers that could survive a Twitch ban
(emphasis mine)
People have never been entitled to a sports career, or to celebrity status by reaching viewers on someone else's platform. These platforms have democratized the "rags to riches" story, but whether it was the '30s or the '60s or the '90s, you've always had to play by the rules of the prevailing media empire. This is no different.
Companies are generally allowed to set arbitrary criteria for who they're willing to work with. There are some very specific exceptions around discrimination against a very short list of protected classes. Other than that, rules restricting conduct are usually legal. Note that I'm not claiming that rules like these are moral, I'm just pointing out that they're usually found to be legal when challenged.
The fact that you can sign up for an account in your bedroom in pajamas instead of signing documents at a lawyer's office in Hollywood doesn't magically make this a public square subject to a different set of rules.