What's a lot easier said than done? Reforming after a telling punishment (like being kept out of the game for two weeks), or starting up a new account?
Because if you know what you did wrong to warrant the punishment, and if you know to be on your best behavior, then reforming should be a breeze. And starting up a new account in a Free-to-Play game is as easy as one-two-three.
As for the relief idea; asking players to arbitrarily do nice things with the promise that they might get their account back would not work. If they got themselves permanently banned, they're clearly not the type to apologize - or if they are, they're not the type to be sincere.
Beyond that, the proposal almost seems like a vainglory, misinformed attempt to manually nudge players to reform well after the point they already should have. For one thing, the phrase "a day late and a dollar short" applies, and for another, you can't just give a player a series of tasks and have them reform from it.
Reform is an act of volition. It's a person's understanding that their behavior is/was not acceptable, and that they need to change. You can't force reform. You can't hardly even provoke it, for that matter. You can only warn of the detrimental effects of not reforming, and hope that players get the message.
When you get punished, that's Riot telling you to shape up. If you don't take the punishment seriously, you're not going to reform. No amount of "go apologize to x amount of players" or whatever arbitrary task you can give a person is going to make them actively think that their behavior was wrong. They need to realize that on their own.
And if they realize it too late, after their account was permanently suspended because they didn't take their punishments seriously, ignored all the warnings, and kept breaking the rules - then that's on them. When they get permabanned, Riot effectively writes them off and says "you couldn't change, you can't stay."
And, lastly; no. Of course I'm not above anger. I'm even willing to tout that I'm always angry, all the time. But having anger and letting anger control oneself are two completely different things. I breathe, I bite my tongue (metaphorically), and I focus and do everything I know I can do to keep my anger in check.
But at the same time, I've got years of personal experience with anger and management thereof under my belt. I can count myself lucky, as some people don't know how to deal with anger.