I would question this point. The captain's vote is a subjective choice, not an objective one. And the one with the most votes is not necessarily the one with the highest rating. A simple example: me. I participated in two team tournaments, in one I was captain #1, and in the other, captain #3, although my rating was clearly far from the top 3. The same hypothetical Gomunguls and LuckyF, based on the vote, could be the opposite, 20 and 1, respectively. Therefore, the spread of captains can be considered partially random. This makes your calculations incorrect, or rather, the opposite, and the balance gives an even number of choices (not players). IMHO.
I assumed that players choose captains based on their rating, that is, the top-1 captain is the top-1 rating, and each captain chooses players also based on the overall rating of the players.
Indeed, if we assume that the captains have a random distribution of ratings, then the expected result of the game in their bracket for each random pair is a draw, and it is precisely with an odd number of brackets that balance is achieved.
