I too was a skeptic of this reporting feature at end game. Get a troll/feeder/toxic player or deliberate afk'er, look at the report option in the end game lobby and decide this won't do anything why bother. Or come to the forums to complain about it expecting more results here.
But for the last few months now, instead of ignoring those who choose to snuff at the summoners code, I've started reporting them and providing as much information as I can for the case in the comment section. On quite a few occasions now, I have received this such notification:
The point is, there are hundreds of thousands(?) of players on the Oceanic server alone, who knows how many active sessions at any given time.
Let's be real about this, even if 1 out of every 5 games played, there was a report put through... how many people would it take to be employed to purely sit down and review every single report case against an individual. Even if it was a full time job? 5 days a week. There would be many man hours required for this task alone, surely.
Yes, there are programs probably written to help speed this process up. Sort out reports in an orderly fashion, only flag repeat offenders etc etc. It still requires human intervention at some point, which in turn requires real time for validation of said report.
So the fact that I have had quite a few of these already in the few months I've been reporting through the correct channels alone, is enough for me to say that reporting people does work. And repeat offenders will be dealt with accordingly.