I came up with this idea a while ago when I came across a post from a rioter, stating that one report was just as effective as nine. I had no idea that this was the case, and I have been playing from 2011. I think that if everyone knew that, nobody would ever ask others to "Report Yasuo for AFK".
My idea is an in-client tutorial much like the combat training showing you around the punishment system. Outlining what kind of behavior is acceptable, and what isn't. It would also show what steps are taken if your account is punished, and what you can do if you are wrongly punished. Target it to new players, and I think we'd start seeing an improvement in the community, as well as with false reports.
You may say this already exists in the summoner's code, and other tools on the website. But I know that when I created my account, I didn't log into the website for two or three years after making the account. Also, as the summoner's code is very broad, it can sometimes be misconstrued, and I've seen some Rioters claim something is covered in the summoners code and cite a portion that _vaguely_ resembles what they are talking about. Making this an in-game tutorial would spread awareness and provide a specific baseline for behavior for players to refer to.
Edit: fixed a typo where I had the word 'ban' instead of 'report' Thanks @The_Highest_Noon for pointing that out.
Edit: By in-game I of course mean in-client, not in the actual game while controlling a champion. That would be silly.
Edit: Keep this post alive, I see a lot of votes on the poll who agree with my opinion but not a lot of upvotes on the post itself. If you vote "Yes! A lot!" please take the time to hit the up-arrow next to the title of the post.