Rather than repeating a problem, here's a possible solution

We currently have a system that rates our personal performance after each match. From my understanding (I could be wrong) this measures kda, cs, skill shot hit percentage, damage/healing/shielding, etc. And I also have heard that it has a way of measuring this in comparison to other players using the same champion in the same role around the same ranking.

If all of that is true, and honestly even if just MOST of that is true. Could that not be a possible way for a computer to measure your non-verbal play? If a player is consistently scoring C's or less it is likely they are either trolling, or that they do not belong in the ELO they are currently at. Instead of "banning" them for this, maybe they could lose more LP per loss with a C or less. If they ARE actually trolling they will eventually get enough reports against them to constitute a ban anyways. If it truly is genuinely just poor play, and it is consistent, than they probably don't belong in their current ELO anyways. So tanking their rating would not really even be punishment at that point, but a chance to allow them a greater chance to succeed in matches. This same concept could be applied the other way around as well. If you get an A+ or higher, maybe a slight increase in LP gain for that match should be provided.

Just an idea on the numbers game, obviously this is the part that would need the most methodical balancing. For both points, I'm not talking anything drastic. Just for brainstorming purposes, I will say the average LP gain/loss for a B performance could be 15 A+ win 17 LP A+ loss -13 LP S win 19 LP S loss -11 LP S+ win 21 LP S+ loss -9 LP C win 13 LP C loss -17 LP C- win 11 LP C- loss -19 LP Anything below C- win 9 LP Anything below C- loss -21 LP

TL:DR- Possibly allow after game rankings to affect LP gain. Not drastically, but enough to help players who are constantly under-performing/out-performing make it to an ELO where the team-play can feel more balanced.