After 2,054 hours of FFXIV (not-including any trial participation donkeys months ago), only one instance springs to mind of me being kicked in a manner that 'could' be perceived as a little unfair.

I entered levelling roulette as tank and the Healer immediately decided right at the start that they knew my limits better than I did, thus ran ahead and pulled three packs for me (to which I happily let them die). They proceeded to call me out, pointing out I was a "bad Mentor" and all manner of childish nonsense, so I decided that if this was going to be the way of it, I would stand perfectly still and let them vent their toxic drivel. It wasn't long before I was kicked, allowing me to instantly re-join a new dungeon with less toxic idiots.

As for people other than me, aside from people being kicked for being largely AFK or toxic, I very, very, very rarely ever see an attempt to kick for unjust reasons. It can happen (with higher risk if everyone but you happens to be a dedicated group of, say, friends, guildies or whatnot), though chances are if someone hasn't done anything wrong, someone will hit NO and keep them in anyway, especially if it's a Tank (less so for a Healer), given most people do want to get their dungeon done rather than kick a Tank and sit around for 5-20mins waiting for a new one.

TLDR: I'm sure it can happen, but if you're going to claim it does so at an obscene level, you're gonna need to back that statement up.