In short, I think Riot cares, its just a really hard problem to solve. Its difficult to differentiate trolls vs simply bad players, or even good players that are just in a rut (read: tilted). Or connection lag and I walked right into their turret. Or someone called in the middle of game and I had to answer.
And its not just a problem in league, the anonymity of the internet creates problems everywhere (see: politics. I won't go any further cuz this isn't the place for that).
But it sure does suck to be matched with trolls, even when they're on the other team. Riot and a few other big games companies (I think Blizzard was at least of of them) made a team together to try and find best practices for removing toxicity from their games. Not sure if anything has come out of it.
They've done some stuff to try to curb trolling, like adding a honor level requirement in order to receive rewards. Not sure how much of an effect thats had, if at all.