Why not add a new system for toxic players?
Why not make it so that toxic players get qued with other toxic players? If anybody can track the number of times you've played a champion, how many games you've played, and the details of every game, why not do the same with reporting? Whenever somebody gets reported they could get a negative reputation score, and whenever you get honor you get a positive score. If you get reported a lot, your reports should have less of an impact on a score. It should also count for the last few weeks of the games you've played, since it would be very easy to just be toxic for weeks, leave, and then comeback having the reputation reset. Everybody has bad nights where they que and they just feel like raging, but there are people who get reported every day, those people should be filtered out.
I know it seems like a bad idea to que toxic players with other toxic players, but when players start to question why they're stuck in the awful place, at least they might re examine their actions and consider the possibility that they need to change. Nothing will stop them from making a new account, but at least if their actions are better, they won't get reported. Reporting counts for something, and honor doesn't really do anything, but at least this would help make use of that.