I was permanently banned around 2 years ago. I appealed and they did nothing (as the rioter stated above). Don't try it as you'll waste time writing a long email.
I'm very sad that you had to go through anger management therapy! You shouldn't have though, and let me explain why.
Going to such therapy means that you have a problem with managing your anger in the real world for very trival things and is affecting your social and occupational life. This game is made with the intention for you to spend a lot of time playing so that you can succeed. It doesn't depend on your intellect, it doesn't depend on how good you are how communicative you are. That's the main reason why people are utterly angry when they lose because most of the time, we know the mistake was not made by us.
It's simple psychology. You aim to achieve something and you give your everything, but when another person comes in and handicaps our success, we get angry, which is a normal human behavior. And when you repeat that step many times, of course you will start blaming the other person. They are the reason why we cannot succeed.
You may say that you don't realize those could be your mistakes but as I said above, this game does not depend on you. When you go in a ranked game you have 4 more team players, which your success is depending on, and if only one them is intentionally trying to sabotage you, that's when you get angry.
This is of course a game, but Riot must know that for many of us this game is (or was) a hobby and we try to make it enjoyable, and something which we could say we're good at.