People go toxic because all they hear is "You suck", "You trash", you Noob" etc. all they hear today is insults, put-downs, degrades and cuts from thier teammates. You Say you dont see it being used? I think the opposite.
They have a taunt/laugh which gets used alot because it is one Keystroke (ctrl + 2/4) and It can be called up instantly.
If they did the same with a "cheer" "Nice job! "Good Job!" "Way to Go!" and made it just as easy to use, I am sure it would be used. If anything I think it would help combat the toxicity level.
If all people hear is how much they suck, How much they are trash, noobs, etc, and other insults focused on how bad they are doing. Then they are more than likely to go toxic. They are more likely to pass that on because they rarely hear someone say "Hey, Way to go! Nice one man!" And often they are most effective at specific moments, the same way a taunt when an enemy dies can carry an extra sting, a bigger jab. The same goes for a quick little "Hoo-Rah!" to bolster someone after they just get a kill.
So you are saying the toxicity breeding more toxicity is a problem that doesnt exist? if so I think you should take another look at the forum boards.
I know if it was implemented, I would use it alot. Its easier to use say...Ctrl+7 to Give your team a little cheer, a little show of aknowledgement for thier efforts. Yes it takes a Long time to write it out, But One macro to show appreciation to your team when they score a kill...when they take a tower, when they get that penta. It goes a long way I think to show that while there is ALOT of toxicity, that thier accomplishments will NOT go unnoticed. and I think that goes a long way to helping bring DOWN the toxicity levels of the community which already have too much hatred. If they can get shouted down and insulted for thier mistakes, wouldnt you like something to bring someone UP when they do something good?
So if you dont see it succeeding, if the idea of raising up your teammates for thier accomplishment is something that DOESNT need to be addressed. Then Clearly you need to open your eyes a bit more and take a closer look.
TL:DR People go toxic because they are shouted down and insulted when they do something wrong, then pass it on. So a quick little command to give your teammates a cheer as a show of support will be very effective in combatting toxicity, I would definately use it....ALOT.
Alot of moments where it could be applied most effectively are missed. But toxicity and flames are ever-present and hard to miss.