i should just have wrote OMG NERF TRBUNAL ITS SO UNFAIR QQ RIOT SUCks
then I have 16 pages of replies and +5millions votes..
I don't think anyone would want a reputation system. The thing is, you know that tons of people are going to -1 that player who they find annoying just because they gloated or something. Gloating is not against the summoner's code, it's not wrong, it just annoys the people you defeated because it makes them butthurt. And there's no easy system that automatically says "your -1 is wrong, it's not counted" (you could devise one but that just adds even more complication).
You've probably seen that case in the tribunal where the only thing someone said the entire game was "lol easier than bots" after victory and all of the 5 enemies reported him for offensive language/verbal abuse. The same enemies would -1 this guy for the reputation system.
There's probably lots of other behavior (e.g. just having a bad game, or being a bit bossy) that would get you -1 reputation while you didn't break the code at all.
And people could just -1 everyone they see because they want everyone else to be punished. You know there are people like that, this is the internet.
The opposite could be true too - a tight knot of people (e.g. high elos, who often face each other) will just +1 each other for no reason every time they play just so they get the rewards.