The major issue with this is and probably the main reason why it has not been implemented already is because a vote kick system is abusable. You could easily vote kick someone just because everyone else is skeptical of the champion they want to play. It is not against the rules to break the meta and they aren't necessarily trolling by picking certain champions. "I want to play Sona mid." Kicked "I want to ADC Gnar." Kicked "I want to jungle Shen" kicked "I'm gonna support with heimer." No... you're not. "Top Urgot." Nope.
Most people who play off meta picks are not picking them to troll, they are picking them because it either can work or they are trying to make it work. As much as I would like to kick the people who join champ select and say "I'm gonna troll this game." unfortunately it will be abused to kick people who don't play champions that others approve of which would ruin the game for many people.
The only solution I can think of is to have a limited number of initiated kicks kinda like rerolls for ARAM. Someone starts the kick and uses their kick and then it is voted on by the other three, if unanimous then player is kicked, possibly 3-1 for success as well (probably best this way so duo Q's can't override everyone else). That person uses their kick but anyone else can vote without using theirs. Even if the kick fails the player that initiated it loses their kick unless someone dodges in which case they get their kick back like ARAM rerolls. Having a limited number of kicks would encourage people to save them for champ select trolls instead of someone who is playing off meta but still intending to do their best to win the game.
You would earn the kicks like ARAM rerolls, possibly able to store two and they would take longer to get than ARAM rerolls.
That's just my thoughts on a possible solution.