The People Want Transparency, Your Honor
Rather than asking us to have faith that reports do something, how about showing us? Those instant-feedback messages were a good start, but they're rather ambiguous. The lack of transparency leaves the whole report system feeling very "...So, I clicked some buttons that I think apply...did something happen, or not?"
As a side-point, since I've seen people using racial-slurs get away with it, and people just being passive aggressive get penalties...I have no idea which reports are legitimate, and what behavior is actionable in the first place.
I understand the secrecy is partly designed to keep people from figuring out how to game the report system, but they're doing that anyway.
In conclusion, a good start would be to provide a feedback message after every report, referencing which game, and letting you know whether your report was acted on or not, and why. This can be done even with a mostly-automated system like Instant Feedback.