First of all, players who behave and don't get punished already get rewards - free stuff from the Honor System (key fragments, ward skins, skin shards, etc. - even special, Honor exclusive skins), as well as the end-of-season Honor Rewards (and qualifying for end of season rewards in general).
If that's not incentive enough to be a good player, then what would be?
Just think about it. Banning players will only lead to new accounts and new accounts, and just boosting players in low divisions by high division players.
And your source for this information is...?
Try to implement something like the player of the week for each division and rank. I don't think that it's hard If you can do it for bad behavior so far. Just by giving honors and thumbs up and thumbs down figure out the nicest, most skilled and friendly players and help them progress.
That would be a needless amount of work, even if you only did it by Rank. The Player of the Week would have to update every week for seven Ranks, whose players could shift in and out of different positions before the week would even be over.
And, on top of that, you would have to have some way to pick which player is the most positive per rank based on data from a week's worth of play. Trying to do that would effectively be a waste of time, since there are multiple more valuable things that Riot can put their resources towards besides putting players on a weekly pedestal.
Stuff like better troll/feeder detection, improvements and tweaks to the IFS and Honor Systems, etc.
And this is all assuming the Player of the Week is just by Rank, not by Division. If it went by Division, that would be twenty-five players that would have to be chosen each week to stand out against the crowd of other players in their Rank and Division.
And God help you if you're going to try and touch Master and Challenger tiers.
And, let's not forget that Riot's looking to to add two more Tiers (and effectively, three more divisions) to the Ranked ladder come 2019, since they intend to add two Tiers and cut one Division off of each tier (putting it to IV-I rather than V-I.)
You could think about something like free coaching for the player of the week, or a nice skin for his main champion because that player really deserves to go further and rank up!
What if the player of the week doesn't want coaching, or already has a favorite skin for their main Champion, or doesn't even have a main?
Trying to personalize the rewards would probably lead to more issues than there already are.
