**Why can’t you give permanent banned players a second chance? You will receive a better player. **
Actually, this is the unfortunate problem. Allowing permanently banned players another chance is an extremely damaging cost. Do you know what the success rate of the Level 20 Challenge was? 5%. Do you know that for each person, they clearly outlined the toxic behaviors and had 1 on 1 conversations with the players to try to improve their behavior? These are players that were hand-picked by Player Support staff because they felt the pleas from these players were genuine. The success rate was still 5%.
Do you know how many games on average these players played? 100 games / month. When a permanently banned player fails to reform, they are creating miserable experiences for hundreds, maybe thousands of players a month. That's not a cheap cost or a low risk and we cannot consciously justify that, for the sake of the rest of our players.
http://forums.na.leagueoflegends.com/board/showthread.php?t=2411284
TL;DR - Unfortunately, they tried this and it was a spectacular failure, as players proved given the chance they'd just go be toxic again. They are not looking for ways to put permabanned players back into the community.