Toxicity Doesn't Breed Poor Play
Yes, it exacerbates it but, in reality it is poor play that breeds toxicity. I think if Riot put more resources into educating people about the game, toxicity levels would decline on their own instead of forcing people to "be nice or else...".
Surely there are trolls who flame and whatever for their own entertainment, but I believe the vast majority of "toxic players" are the hyper-competitive type whose goal is winning. People really have no reason to flame outside of the actions/play of another person.
It's entirely possibly people "have bad games" but there's a difference between poor individual play and poor team-play. Having poor team-play / game sense is separate from one's own skill on a particular champion.
For example: When does most flaming occur? It's generally when someone keeps fighting 1vX, overstaying and dying after a push, or being completely oblivious to objectives (most notably the ADC who stays bot CSing while the jungler and support go for an early dragon after having killed the enemy bot lane). The dragon example is a common one even at the platinum level. These issues have nothing to do with "having a bad game" as they do "decision making". Your individual decision making does not automatically leave when you're on an unfamiliar champion.
It's indisputable that it's much easier for one person to ruin a game than it is for one person to carry it and this is solely what causes flaming. Someone who is 2-0 or 3-0 early on in mid lane can be considered to be doing well, but that is completely erased by the 0-7+ by 15 mins bot lane. So if Riot takes a more aggressive stance towards improving general game knowledge for the playerbase I think toxicity will decline.
TL;DR: Riot should more heavily explore avenues of educating the playerbase in terms of game knowledge / proper play and toxicity will likely go down on its own because frustration comes from having "that guy" lose you the game by themselves.