First, Riot does care about trolls, but the issue is they're extremely hard to detect. You have to prove that they were doing something intentionally to screw their team over, and when it comes to gameplay actions, that is beyond difficult to prove.
Detecting chat related offenses (flaming, for example), is incredibly easy. Nobody here likes dealing with trolls, but, chrissakes, man. Don't you know the first rule of the internet? Don't feed the trolls. You may not be able to stop them from trolling, but you can sure as hell keep your account safe by not giving them the reaction they want.
Second, you don't seem to understand the incentives of the Punishment and Honor systems - moreover, you're misattributing things and making a fake argument about them.
The Honor System incentivizes good, sportsmanlike behavior with the promise of rewards - access to ambient key fragment generation, periodic rewards caches, Honor flairs, exclusive skins, and, ultimately, End of Season bonus rewards. (On top of Honor 2 starting to become a prerequisite for some things, like End of Season reward eligibility and eligibility to enter Clash Tournaments).
The Punishment System dis-incentivizes bad, unsportsmanlike behavior with punishments and harsh repercussions for breaking the rules, like chat restrictions, suspensions, and, of course, being stripped of Honor.
Does this mean that some assholes are going to ignore the incentives and try to get people punished by breaking the rules in a difficult to detect manner? Somewhat - it's inevitable that there'll be a few bad apples 'midst the bunch.
Does this mean that, because those assholes exist, that the systems incentivize bad behavior? Hell no.