Inactivity in chat should be bannable (maybe one warning, but still a very serious offense).
I called top lane and locked in as Jax with 5 seconds left to choose. Nobody had claimed top lane yet. When the game started, I went to top lane, but Heimerdinger followed me. Mid was wide open. He then proceeded to steal all my CS and one Champion kill (although this wasn't really his fault, it was his turrets' fault for that). I then told him to go mid, where he had been unanimously assigned by the 4 other players on the team, since he locked in without claiming. He never responded for the entire game. I ended up having to go mid against a Nocturne who had 5 minutes of a free lane because he stole top. although that's not my problem. It's the fact that he seemed to be able to play the game decently, but ignored everyone's requests to move as if he couldn't see the chat at all. Everyone has played with one of these players. These people are everywhere, and nobody seems to care about them. In my opinion, they should be IP banned for life, although my guess is that's a little too extreme. My point is that League is a team-based strategy game, and players who lack the required basic communication skills should not be allowed to play such a game.
My proposal is that any player who is inactive in chat be warned not to ever do that again, and then the next time that player is inactive in chat, the player will receive a temporary ban for maybe 4 hours. (Yes, this is more serious than Leaver Buster, and this is for a reason. Players who leave games usually don't want to leave, but a player who refuses to listen and communicate with teammates is much more of an annoyance for teammates than a disconnect.) For ranked games, instead of being a temporary ban, it would be a ban from ranked for the season, as Ranked should be reserved for only the players who know the game very well and want to prove it.
Let me know what you guys think about this, along with similar stories about players like this.