its mainly automated, the system is able to filter out the false reports. So its not just "3 strikes and you are out". It actually takes alot more than 3 games to punish someone, and the system looks at the 90 day / 60 day / 30 day history as well when considering punishment. So it's a little but more sophisticated than you think.
For the players that have alot of reports, yet aren't punished by the system, the Rioters will manually review the game, which is when the notes are actually useful. It gives the Rioter's a perspective of what you thought wasn't acceptable, and their pair that with what the rest of the community thinks. Keep in mind that not all reviewed games automatically means "punish".
Then again, you don't need to write an essay of what is happening, they can see the gameplay (including the button's pressed - like if you pressed "S" to purposely stop an AA to let a kill go, the click locations, apm, etc etc), the chat logs (including pre/post game) and the account's history.