I don't think you should even compromise on a vote kick function. It belongs in the same trash bin as having labels with roles you can play.

Champion chat in Tribunal: Thousand yes, it would be incredibly useful.

Chap select chat would be very nice for reporting bad people, but it's still an "after the fact" problem. You either dodge or suffer before you can report the toxic behaviour- sometimes for over an hour. That's a potential 1/24th of a day lost to some troll who feeds or otherwise trolls the game for no other reason but to troll. A pre-game report feature that functioned like a dodge in that it removed you from queue and allowed you to type up a report about that person- with the pre-game chat log attached as proof and a way to double check claims- that doesn't carry with it a massively high dodge penalty for Ranked, possibly the same penalty for normals, 5 minutes- so you aren't stuck with a troll would be, I think, best. especially if you add a delay on report leaving (10 sec. timer added on top of everything else?) so others can also input a report before the queue is entirely closed. To combat groups of people abusing it, perhaps add a "who queued with who" color difference of something of the sort.

what exactly do you mean by group finder?

If you mean that you'd declare your role and find gorup that needs it- this would help alot in solo queue.
If you mean just finding group of people thru chat, it wouldn't change much.
Mostly becouse it would be just too tedious and you'd still have random people for just 1 game.

This vote - kick would be really more harmfull than help. Ability to have group fitting your preferences on the other hand would help avoid alot of argument and frustration due to playing roles people dont like.

Champion select chat in tribunal would help. Group Finder is not such a good idea, they idea is that if you can play different roles you are rewarded with better rating.

People that only play one role and one champion would be the ones who would benefit from a group finder option, I dont think its a good idea.

I think a group finder idea would work incredibly well, so instead of queueing and having 5 people who all fight over mid lane ending in a dodge, people actually queue for their roles.
However, certain roles such as support may not be queued for as often, and queues will probably increase.

In my opinion "Champion Select Chat in Tribunal" would not only displace the need of a "kick vote", but would be superior to it.

If by "group finder", you mean being able to select roles before queuing up, then yes, please. It's long overdue.

As I understand it, Riot's biggest problem with this idea is that it would "force the meta" on people, but I find this to be a bad reason honestly. 99% of the time in ranked, if you don't play according to the meta, it's going to tick off your entire team. If sometimes people were okay with it, the fact that this hasn't been done yet would be a little more understandable, but they're not. This system would not enforce the meta any more than the players already do, but it would make the game much more playable for those who only prefer a particular role and lead to less conflict in champion select.

This is a large part of the reason why I don't play ranked at all (or rather, why I rarely play League at all unless I'm queued up with at least 3 other people) - mid is the only role I'm good at, and it's the only role I have a desire to play as I dislike other roles. I have three choices: force myself to learn other roles at the cost of my ability to enjoy the game, deal with constant arguments and dodging in champion select, or often play a role I know I'm bad at and lose the game. I would be much more excited about playing LoL if I didn't have to worry about how stressful it's going to be just to get into a game.

Normal game queues could be left the same as they are now, since people are more okay with experimentation there.

Group finder as in some kind of pregame role caller? Or group finder like a find 4 people to queue with option... because either one sounds a lot better than what we have atm.

As for forcing the meta.. You could revise general terms champions are classified under... In DoTA everything not a carry is a support, but in LoL there are so many roles, jungler, pusher, support, bruiser, carry, mage, which aren't actually "meta" they are just classifications of a champion.

If players had options to pick what kind of team they are looking for you could have some type of team builder, this would work even if the meta changed.

Example, I would like to get matched with : Support, Jungler, Pusher, Mage, I will be playing Carry...

But that wouldn't limit them from putting into the system "I would like to get matched with: Carry, Carry, Jungler, Mage, Pusher" for different compositions... And this doesn't even mention lanes, so no big deal that can still be discussed in chat..

A system in which you could rank your preference on roles or abstain from ranking certain roles to match make groups would save a LOT of rage, and prevent a lot of dodges, it could make Queue times go up, but then there would finally be an incentive for someone to want to play support, faster Q times.

So for instance I start gaming I like playing mid / top, don't mind support or jungle, don't like ad carry, I could do something like :
mid 1
top 2
support 3
jungle 4
adc

Then the match maker would proceed to look for groups that have openings in that order, showing me an icon for what role I had been selected for, and then randomizing the order of the picks so that picks and counter picks wouldn't be controlled by the system. In this example I would never be asked to play adc.

Would a system like this solve every problem, no. There will always be trolls, or someone who forgets to change their Queue settings. However this prevents: "Well I'm first pick", "but I called mid, I'm gonna pick teleport revive ap nasus" in most situations. Not to mention it would also help to continue to quash reports of elo hell. One of the big arguments being that you get screwed into playing a role you're not good at which further skews your likelihood of "getting out". Furthermore then the people who insist on only learning how to play annie then deciding to play ranked, won't screw their team when they get forced to jungle and the only champ they really know how to play is annie (though jungle annie OP). Anyways, it's definitely something to consider.