You've just told players from both teams that you are choosing sides. Is that what you want?
That is being intentionally inconsistent. Is that the reputation you want?
Maybe not, but it could have. Suppose the batter hit a walk-off homer on the next pitch (the one that was going to be your FYC). Now what does "your friend" F2 think? A player who should have been dumped just cost his team the game. You now have lost credibility with both teams.
If you want to send a message, dump the batter. Do you think he will "get it" any more by allowing him to stay?
My bottom line on the FYC: don't do it. If he crosses the line, toss him on the spot. The message can't be any clearer.