So, to start off with, your post is titled (and has at least one mention of) reporting in Champion Select, but it seems that the majority of the post is dedicated more to the subject of vote-kicking. It's a small issue, but still worth pointing out.
On the subject of Vote-kicking - this is not an option, period. You've already pointed out some of the biggest flaws - groupthink antagonising off-meta picks and anti-social behavior. I can tell you now, vote-kicking is not a good option; I've played World of Warcraft, and I've seen a great many people kicked from groups for arbitrary reasons.
And League of Legends, unfortunately, would not prove to be an exceptional case in that regard.
On the subject of Champion Select Reporting - I've seen a great many people propose the idea of reporting in Champion Select, but I've not seen a single person actually elaborate how it would work. I don't know if it's just from a short-sighted supposition that Champ Select reporting would be the cureall to their problems, or if they believe that validating a report from Champ Select would somehow give them free leave to dodge the match without penalty, or if the issue is somewhere else entirely, but the point is; nobody seems to actually consider what they're proposing.
So, let's run through a couple scenarios to see how a report feature in Champion Select would even work, and the problems that would arise from it.
- Report Queuing - let's assume that, since the IFS requires a match to review, that the CS report feature would only queue an automatic report (or a prompt to report) in the post-game lobby, and that you still need to play the match all the way through. It would, for all intents and purposes, be generally functional, but there are two big problems;
First, accurate reporting requires accurate knowledge of the misbehavior, and you typically can't get a good read on what type of misbehavior will be done from Champion Select. So, if you just arbitrarily queue up a report for hate speech, fullmute the player going into the game, and leave the match after your automatic report goes through - nothing's going to happen if that player didn't use hate speech.
Second, I generally have to assume that the goal of Champ-Select reporting is to avoid playing matches with people you know/assume are going to misbehave, so, being forced to play the match out regardless to get the report filed is generally going to be counterintuitive to what I assume the goal is, and leave people with a bad taste in their mouth.
- Punishment from Champion Select - So, now let's assume that the system is designed in such a way as to punish people for their behavior from Champion Select, without needing to play a match out. Right now, I can already tell that such a system would increase the likelihood of players dodging, if there's an indicator for whether or not a report is validated. And, as ever, there's a bunch of problems with this idea;
Chat misbehavior is the most easily identifiable offense in League, and it's a no-brainer that there will inevitably be people out there who'll troll and bait flame or ZT chat to get someone punished. Give them the ability to do so without even getting into the match, and you've got a recipe for disaster. They'll bait out flame or ZT chat, report you, get the notification, and bail before you can even react. That is not a good scenario to have on your hands.
Beyond that, though, there's also the implication that, for whatever reason, a report system in Champion Select would be able to identify trolls (somehow any better than the IFS itself does); so, we have to ask, what should the system define as trolling? You can't ban off-meta picks, since Riot doesn't want to force a meta, and you can't punish someone for banning someone's pick intent, since as a general rule, bans > picks.
You'd have to have the system look for signs of obvious malice with those decisions, because trolling is more than just a stupid pick or a wayward ban. And, since Champion Select has less ways to troll than in a match, the system would have much less to go off of for cluing into trolling behavior.
And, of course, there's the issue of dodging. No matter which way you cut it, having a report system that punishes people before the match even begins is going to encourage people to dodge - especially if you give them reduced/no LP losses for successfully reporting. You could try to avoid the issue by not showing the punishment notification, but that still leaves you with people who'll just report and dodge without thinking about it.
At the end of the day, a report feature for Champion Select isn't really an option. It's either counterinuitively designed, leading to inevitable pain and frustration on the part of the reporting players, or it becomes a broken, exploitable, detrimental mess that causes more harm than it does good for the game.