You know, if you want "toxicity" to go away...
Then stop making such a big deal about it. Hell, I'd never even heard the term "toxicity" outside of scientific context until I started playing League, and I've been playing online games since Diablo 2 and Runescape were big.
But, as long as the community (and Riot) makes such a big deal about "toxicity" (which, by the way, is actually very, very, VERY common behavior in many competitive settings, even some professional ones, to the point I wouldn't use a word with negative connotations like "toxic"), it's never going to get better. The more negative attention that surrounds the whole thing, the more attention-starved kids are goinna freak out about it. And I'm not just talking about the people being punished, I'm also talking about the people who act all holier-than-thou about people who get banned / chat restricted, and join Tantrum with "smiting" people like an asshat. They become hyper sensitive and spur on the trolls when they freak out about chat or something, and it just creates a big loop.
So, you wanna fix the whole "toxicity" issue?
Step 1: Fire Tantrum. Smug asshats like that are not going to make a single player behave better. All he'll do is create more issues.
Step 2: If a player is chat restricted in the game, or banned, do not allow them to post on the forums. If you can't do that, then just delete any post with people complaining about being banned (unless it has a good reason to stay up).
Step 3: Rework the escalating punishment system. Make the punishments painful from the start, but not too harsh, and make them relevant to their offense. Someone is trolling or feeding? Put them in a 20 minute queue for the next few days. Someone is being an asshat in chat? Just keep the current chat restriction system. Someone is scripting or boosting? Just ban them outright. Don't be lazy and say you can't track things, because you absolutely can and have shown you can on multiple occasions.
Step 4: Stop talking about toxicity. Don't give it any attention or thought, and just let the system quietly do its job. Also delete player posts talking about toxicity.
Step 5: If reform is actually your goal, then hire people to talk to people who are repeatedly being punished (according to you it's a VERY small number, so you can't say you don't have enough people) and try to help them with their issues instead of just outright banning them, then having them make a new account and becoming even more of an asshat.
Been playing MMOs for many years now, and I've never seen a community so entirely asinine as League's is. But that's because both the community and Riot encourage it.
So, if you actually care about the whole toxicity issue that's been bubbling up a lot, do something about it. But then, I don't really believe you do care, since banning someone means they have to re-buy skins and all that. You're certainly welcome to prove me wrong though.