Recently I've played with someone who put down people the entire game. He trashed on me after the game even though we won. I reported him but to me it feels like nothing ever gets done. There needs to be some type of system to where we can know if they got banned. I feel like nothing happens to people like that.
Typically you don't just jump straight to account bans for a first punishment, and you usually aren't punished for the first offense either; it takes multiple games of being reported and the reports verified. So even if you report someone and they keep playing, that doesn't mean they won't or haven't been punished.
We also already get notifications for this, but only when our report triggered the punishment, and we don't always get it. It's not helpful to anyone to directly let you know that a person is being punished (Riot is against name & shame). Also, if you got a message every time someone you reported got punished you'd be randomly spammed and it'd just be extremely annoying.
