TLDR - Automute verbal abusers, those who harass and those with negative attitude. Being muted is a punishment.
In reference to this post, I would like to link you to Penny Arcade's video on Harassment.
In short, players who continually spew verbal abuse, have negative attitude or harass others should be auto-muted in game to all other players for a period of time (a week or so) instead of, or in addition to, receiving a time ban. This WILL NOT affect champ select, but WILL affect in game communication.
Think about it, a player is verbally abusing and harassing others. They receive a time ban. They come back, and continue to abuse and harass. They receive another time ban. They come back and then are Permabanned. They create another account and the cycle starts again.
They may not be bad players. It's just that their behaviour which is deplorable. Instead of just being time banned for a few days, and allowing them to come back to verbally abuse the community again, why not auto-mute them to all players.
Sure, another player can CHOOSE to then unmute them (however, they will probably know what to expect). The player is still able to ping (to communicate MIAs, etc). Perhaps a list of shortcuts could be implemented to common phrases (MIA, Defend, Attack, etc) so they can still communicate. The player can still PLAY the game. However, they WILL NOT be able to insult, abuse or harass the community.
This won't stop trolling, AFKers or bad players, but it will be a step in the right direction to solving the problems with the toxic community.