80 million active players per month. But some of them are alt. accounts. So we don't have the exact numbers.
There is also the issue that the work load does not reduce. X part of the 80 million are the same people who continue being toxic over multiple accounts. Riot bans accounts but not the people playing them. So the 'X' part of the 80 million is going to remain consistent and this work load will not reduce unless some of these people decide to stop playing the game after being banned on their accounts. As a result, manual labor is not going to come into play anytime soon. All they can do is deal with this using their current scan system and # of reports accumulated before being reviewed.
Riot's choice presently is to continue allowing these toxic players who have been banned on their former accounts to continue playing the game. But is that the better option? The X number does contribute to faster Q times, even matchmaking but to what point is this tolerable? In exchange, they are continuing to deal with potential toxicity and poor gaming experience for the 9 other players.
There there is also the fact that these banned players learn to take advantage of loopholes. Whether on accident or learning from others. For example, griefing. Intentionally feeding but not making it obvious. Saying stuff that isn't ZT but intentionally misspelling some racist slurs to get their idea across. Or even being vulgar in a way that isn't punished.
Overall, OP. Manually reviewing reports will probably not be in their agenda anytime soon unless they start banning people from playing their games for a fixed period of time. Because, no matter how much $ they dish out, they aren't reducing the toxicity because these people have free reign to keep returning. All they are doing is facilitating the handing out of appropriate punishments so this turns into a long drawn tug-of-war on whether the player behind the banned account is now reformed. Whether he refuses to reform and then quits after his 7th banned account etc.
I also noticed that the basic age for playing League is 13 or older. Do you expect someone younger than 18 to be able to keep their mouths in check? Or even adults. Maturity doesn't really have an age limit but most of these young kids wouldn't exactly be able to control their emotions. Most of the 'I got banned back when I was 13-17 years old- and want to get my perma. banned account back' threads make me question this age limit. Of-course, Riot probably has no way to know someones exact age behind their accounts. But this was just another observation.
I think that they need to drive the idea that winning is important out of the community's mindset. Most of the arguments etc. happen when someone misplays and it makes one think, "Now we might lose!" Its better to ingrain a mindset like, "Enjoying the game is more important." Because, winning is so important. There are even friends who refuse to play with each other after a few years. I saw a thread the other day where some guy was talking about his friend claiming that he was 'cursed' and would always break his win streak.