MVP System
Implementing an MVP system into the game would decrease the amount of trolls and people who don't try their hardest.
After a match, the opposing team members each choose a player from the other team to vote them the MVP. The MVP gets a small reward like extra LP or IP (maybe RP?). People would be inclined to get this MVP spot so they really try in the game.
You could also add maybe an icon tracker of how many times you have gotten MVP to show off to other players. This could replace the honor/teamwork system which really doesn't have an affect except for the possible banner.
Getting MVP would really make you enjoy LoL a lot more and gives the players an end goal.