It does work. If you spend enough time here on the Boards, you will have seen a fair number of cases where bans were either lessened, or overturned because they were found to be a situation where the IFS issued a ban based upon a player repeating toxic phrases, or a player who was jokingly reported by their friends. The vast majority of the time however, the players who are writing in to Support appealing a ban have a legitimate punishment because they were either a. actually extremely toxic or b. mildly toxic but were on the last punishment tier, and are rude and demanding when speaking to Support. In neither of those cases will a ban be removed, and players should not expect it to be. Without seeing the original poster's logs, and knowing whether he had any prior punishments, it's impossible to tell whether his ban is warranted or not. But you are disseminating false information when you use a blanket statement like "Sorry, doesn't work" and we try to make sure that people understand the correct processes and reasoning behind them here on the Boards.
And I've read your manifesto. I refuse to dignify it with a response. I followed the advice that we give everyone here on the Boards with regards to trolls: mute (in this case read and ignored), report, move on. With all due respect, I wouldn't even have replied to you here, as this seems like just another way for you to spread your pervasive trolling, but you're giving this OP false information, and it's not right for someone to come in and simply crush any hopes he may have when you don't have enough information to make that determination. So, I've replied to correct the fallacy.