Unfortunately it has been proven that they don't review the posts or the requests on reasoning for chat bans.
-The new system got tested (albeit in a hateful and wrong way) by trolling other people and testing how many times they got reported.*hint* search google for chat ban tested *hint*. The new chat system is simply by how many times you got reported in a given number of games, NOT for what or how you say it. One of the best parts that interested me is post chat. They didn't talk for the ENTIRE game. In the post chat they did the typical "wow that build is so dumb" etc etc. The normal frustration of losing. NEVER using slurs or cursing. (you know things that SHOULD be banned for).
-What is the end result you ask? They got banned. They got banned because they said "your build sucks" in POST chat. They got banned from talking during a game, in which they said NOTHING, because of the global aspect of internet anonymity the world has grasped so dearly on to and the comfort of that god forsaken report button.
-Now for the other side of the coin. In games they won (even though they were trolling) they got reported 84% less than the games they loss. 84% Riot, 84%. So sit down and really think about that. Everyone sees the tips Riot gives us at the loading screens. "People who curse lose 35% more games". I have statistical PROOF that it is "People who lose 35% more of their games, curse".
So Riot, I will admit I seriously doubt anyone important will see this measly post from some nobody of importance or fame, but if you do, I challenge you. Prove to your forum viewers and myself that the system works differently. Prove to me that you actually care about the community of League of Legends that I devout so much of my time playing. Prove that you aren't using a computer based percentage comparison program to decide who has the luxury of being yelled at during a game and who has learned that you are better off instant muting your entire team.