Ok i know i'm gonna be in the minority with what about to say, but please at least take the time to read and consider my statements here before jumping on any bandwagons and dismissing me.
For starters, Toxicity will ALWAYS be a problem in gaming, sure we can add and implement systems to fight it off but no matter how hard you try there will always be toxic people, and the BIGGER community is, the more you are going see. Because just like in games, in real life we have punishment systems in place and we still have toxic people IRL too. it just aint ever gonna go away.
While yes, there are things we can do to fight it and try to minimize it as much as possible, but the only TRUE way to really get rid of toxicity would be to delete the chat (or since we can't MUTE the player) Now i know you said that "muting" only hides the problem BUT actually it really does more than this. Hear me out for a second, Muting does a few things here. 1: it makes it so you are no longer exposing yourself to the harmful words of the other player, you already know they are a jerk so now you no longer have to see it. This is good because 2: It also prevents you from caving in and FEEDING him or her the Attention they are ultimately seeking. Weather you are being toxic back when you respond to players like this it just gives them more fuel to keep talking and to keep responding. you already know they are toxic, and by edging them on you are now part of the inherit issue, instead ignore them, and at end game ask for people to report. typing in all chat and during a game and talking to them is ALSO being toxic, because now your making the situation more involved and bringing not only your game play down but also morale down as well and thats not good.
Honestly i always felt riot should have made a option in game to turn off chat completely, we now have Emotes / Pings to communicate well enough with players that we DONT NEED chat function, which is where MOST of the toxic behavior happens, (why do you think games like hearthstone dont have "Toxic" players being complained about 24/7?) The Chat is the real demon, when you give players a way to aggressive channel their frustration onto other players, and human nature is immediately to DEFEND themselves, you now have a chat full of players constantly bickering, at this point who ever started it no longer matters, you both get punished.
It may sound like a cop out but honestly the TRUEST way to battle toxic players is to honestly ACTUALLY ignore them, the more you shine a light on something the more its gonna start appearing frequently and MOST people when they start being rude or angry are legit trying to get a reaction from you, if you dont give the reaction they no longer have anything to talk about and if all 9 other players ignore them ... then they just talk to themselves ... and the other 9 players live in peace.
For your next experiment, try muting EVERYONE start of the game, for a multitude of games and use pings / emotes to communicate and watch as your skill and FUN levels improve, once u gain control of how YOU respond to toxic people by a INSTANT mute rather than "Typing" back you realize that the games 10000x more fun when you use the mute / hide the chat