This system existed.
The Tribunal was great. I started playing in Season 1---toxicity existed, sure, but compared to today it was substantially less. The old Tribunal system had it's drawbacks in that it took longer for cases to be judged and punishments to be administered, but the upside is that the community was able to decide what the standards for punishment were.
Let's be totally candid here also, a computer just can't determine every type of bad behavior---I remember many cases in which a player was engaging in passive aggressive type of behavior and the vast majority of peers agreed and they were subsequently punished, while the fancy computer system can't see that. Example: My teammate gives up first blood, another teammate types "Good job!" in team chat.. clearly the intention was to shame the player for making a mistake---but an automated system sees "good job" as being encouraging. You might argue, "But the system could be programmed to punish that behavior", maybe but if there was an exchange of deaths that occurred on either side then the water becomes a bit more murky. Still the people in the game could better ascertain the context and would have reported it appropriately. A group of peers could better determine if it's toxic or not.
There are countless other examples of situations where a human review is far better than an automated system. However, Riot opted for an automated system that catches the most egregious of offenders while leaving trolls that have learned how to game the system to roam free. Trust me, I have many such examples in my browser's bookmarks list of players that troll, intentionally feed, are passive-aggressively toxic (taking the junglers camps, taking roles by forcing their way into lane (despite being assigned support for example) and other offenses that go completely unpunished.
At one point in 2014/2015, Riot told us that the Tribunal was coming back----unfortunately like many things Riot says, this has turned out not to be true.
League of Legends is an amazing game, it was created and designed well initially, but the community is increasingly terrible and the current behavioral management of the community has obviously given up or simply doesn't know what to do any longer with regard to handling the behavior issues.