And the person that essentially intend and afk pushed went unpunished?
afk is handled by LeaveBuster. It is an automatic detection system. It does not required any report to work. If someone goes afk, he will be reviewed by LB. If he has a record of frequently leaving games, he will be punished according to the LB punishment ladder whether he is reported or not. LeaveBuster is probably the more reliable system in regard to punishing someone over the IFS and feederbuster.
Basically I got tilted at the end of the game and after LITERALLY EVERYONE LEFT THE GAME I went off... And I got banned for it. SOMEHING THAT NO ONE SAW AND THAT BOTHERED NOBODY. I believe this to be ridiculous and that I should have my bank repealed.
Chat related punishment is handled by the IFS, Instant Feedback System. This system required user report (unlike LeaveBuster) to work. If no one reported you, you will never get reviewed by the IFS and you will never be punished. If everyone already left before you unleashed your vent, then who would report you? You must had done something or said something either during the game or in pre- or post-game where there are people who had to read it and something toxic enough that they feel compelled to report you.
If you want further discussion, you will need to post your unedited, complete chat log of all games in your report card.
If you want to appeal the punishment, feel free to submit a support ticket https://support.riotgames.com/hc/en-us