I don't think toxicity is a problem. If people want to be dicks, let them be. That's just life, some people are nice, some are not. As long as they're not griefing or cheating there's no real harm. If people can't handle some mean comments maybe they shouldn't play an 18+ game about killing each other in which even NPCs and pedestrians swear.
Blizzard has been trying for a long time with Overwatch like you said and I still see people trash talking in almost every game, even on GM level. Forcing people to be nice isn't really gonna work, they're just gonna find a different way to be toxic.
I recommend to stop getting offended about what some random immature people said on the internet. It really shouldn't be that hard, unless you think they're right, in which case maybe it's not really that toxic after all?
Also Twitch has nothing to be proud of. Banning people because they said a word? Like, what? Soon we won't be able to talk at all, we will just be spamming smiley faces and hope the other side doesn't get offended because the smiley has a different skin colour then them.