As someone who has received multiple permanent bans over multiple games, I feel I am a somewhat self taught expert on the matter.
Ill start by pointing out the flaw in chat restrictions. Its pretty much go play 10 games of ARAM. No one learns anything from them. It is just a temporary mute button for a few players. You just play 10 short matches and go back to being toxic in ranked. The goal of them is to get rid of them as soon as possible. A minor inconvenience.
Next is the permaban. When I log on and find a permaban waiting for me (not just on LoL), I laugh about it, relive the good times thanks to reform cards, (lookin' at you Rito Lyte <3) and make a new account. Get it to 30 in a week, and back to being toxic. The only thing I learn from permanent bans is "Less micro-transactions, this is only a temporary account". Permanently banning someone and wondering why they don't change is similar to wondering why people jailed for life without parole don't change. You've done your worst. That's the biggest punishment you can do. Take away our account. We just make another one, knowing that there is nothing you can do to stop it. The worst part about being permanently banned is having to think of a new name.
(By the way it would be sweet if perma-banned accounts got their names taken away to free up some names, consider it babes)
There was even a time I would have 2-3 level 30 accounts sitting, waiting for that day when I get the permanent ban. 30 seconds later I'd be back on the Rift, only difference is, having just lost an account I was pissed off and more volatile towards players.
However if I find that I have been banned for 14 days, I spend those 14 days waiting to regain access to my account, because it isn't worth leveling a new character/account for only a few days of play time. In that time, I have time to reconsider my actions and it actually feels like a punishment. It is always on your mind, you sit there wondering what game to play and if you have a craving for some Summoner's Rift, you can't play it.
They send criminals to jail with a chance of parole to invoke a change. They can use their time away from society to change their behavior and become a model citizen. You can use the same in games. I believe that 30/60/90 day bans have more impact on toxic players than a perma-ban does. You need to break the habit of abusing people, and permanent bans don't do this.
Toxic players are degenerates. We are lazy, but also determined. We can get a new account to 30 within a week, but we probably won't level a new account if we know we can get our accounts back after a month or two. Who knows, maybe in those months we might mature enough to start respecting our fellow summoner, but we certainly won't mature very quickly in the 30 seconds it takes to recreate an account. All we learn is "don't buy Riot Points cause we can lose our accounts at any time."
A decent method of re-education would be a parole system of sorts. Give people a reason to change. People who have received lengthy bans (90 - permanent) could have the opportunity to redeem their accounts by participating in a trial period. The trial period would only be shown to the player. The player would then play a games with other summoners in good standing (players rarely reported, often honored).
If the player successfully plays for a predetermined period without becoming toxic, they would redeem their account. If the players fails to be civil and receives a report, the report would be investigated and decided upon. If the report was valid, that account is permanently thrown into oblivion. If the report was unwarranted, the account continues with the trial. This method forces the toxic player to undergo a time period where they would be exposed to only good behavior, breaking their habit of abuse. This would be a one time offer, for obvious reasons.
Give toxic players a reason to change. Make them use their time away from the Rift for something more than leveling an alternate account.
That's how I see it anyway, and I can safely assume I have experienced these punishments more than most people.