Once a month doesn't seem like it would bother anyone, and it would be quite useful. Knowing how many of our reports are labeled as false would make a lot more people trust the system, and having the chat logs of the games where the report was deemed as accurate would help us identify attitudes the community dislikes even if we haven't been punished. It would also let us send messages to Riot Support with inaccurate accurate reports, to help them improve the system.
It would probably also make people less surprised about incoming punishments - if the monthly status card says that your account is in poor standings, then people can try to reform and better themselves without even needing to be punished. Likewise, if you've been punished recently and then the monthly status card says you're in good standing, you can feel good knowing that the system has recognized your reform.