Reformation and Permanently Banned Players

This is a followup for the question the support team answered, about toxicity and reformation.

I submitted this in Ask Riot just now but wanted to leave it here as well. I see quite a few people in game that say they have been permanently banned for toxicity, but they don't seem to be very toxic on their new account(s) when I play with them, what happens when a player who was perma-banned creates a new account and uses it, but not in a negative way? The player shows genuine improvement and positive play all throughout their games, are they still held to the same mistakes that they made in the past, and their present progress simply ignored because they were banned.

I'm very curious about this, thanks to any Rioter who responds, or even player in general. Maybe I can see the community's opinion on the topic.

Thanks!