Honestly, I don't think a Vote Kick system is going to happen (since, again, easily abused and also runs counter to Riot's goal to get players into the game ASAP), but one of the biggest problems I see is that the concepts aren't remotely developed past the "group votes to kick player, requeue follows".
Even disregarding the abuse cases, this is something where you really have to ask more about it; like, when does the Vote to Kick option kick in? The pre-selection phase? Ban phase? Pick phase? Post-selection?
How many votes should it take to clear and boot a player from the match? What's stopping people from throwing up a vote at random with no context provided? If it takes four votes, what's stopping premade-abuse?
Should the Vote Kick be somewhat similar to World of Warcraft's, where a player starts a vote, provides a note of context, and has all but the target player vote on it?
And, depending on the timing of the Vote Kick, what would stop people from booting teammates who ban another's pick intent, or who play something off-meta or sub-optimal? What would stop people from scouting their teammate's winrates and voting to kick them for being under a certain threshold?
These are just a couple of the things I think go more or less ignored in the making of some of those Vote Kick posts, and, while I still ultimately believe that a Vote Kick feature wouldn't be added, it's still certainly worth puzzling through those questions.
Hell, maybe someone could even blindside us with an answer to the abuse cases.