Mute for chat offenses, ban for gameplay offenses.
If you ban a toxic player who's addicted, they're going to make a new account that they have no attachment to and toxify low level games. Riot is already having a huge problem retaining new players, and I'm willing to bet that's a big reason why. Letting very toxic people continue to play but taking away all chat privileges for several months would be better for everyone. If they act out their toxicity in game by inting, then you can perma them.
Riot needs to also have a much clearer path to reform than they currently do, with more feedback from the system and more positive reinforcement. More little popups that say hey, you're making progress, keep it up, or you were just validly reported, chill out before you get banned. I've played 80 games since being 2 week banned and I'm still checkpoint 0. No idea if I'm making any progress at all. All i type is rawr, xd, and gg.
Riot Blaustoise agrees with me before all you puritans pile onto me. :)