So the point of not reporting chat stuff, is to lessen the amount of shit that Riot has to sift through? But most chat offense punishments and reports are handled by an automated system, so if I were you, I would stop convoluting your master plan with an extra pointless step. Just rally the masses with your vigor to hunt down these trolls and not let them go. Leave the "dont report for chat" part out of it. It doesnt add a mess for them to sift through. People can do both and it will be equally effective (or ineffective).
I do like the idea of people being driven to bring trolls to justice. Maybe if 50% of the playerbase was more adamant about it, Riot would almost have to step up their game. Thousands of tickets about how "i reported this troll and here he is trolling in my game. Please clean this mess for your playerbase, its ruining your game!" It could be glorious.
But as a 32 year old disillusioned man, I feel this wont happen. People are complacent. Lazy. Its a video game. This is a leisurely activity. Not enough people will care enough to take extra time to do this... myself, unfortunately, included. If I run into enough trolls to ruin this game for me, I will simply play something else. Its really not a big deal to me and millions of other casuals like me.