I submit that the mission did turn out to need McCoy, since it was McCoy who helped knock some sense into Kirk and make him realize that he was letting his ego get in the way of the good of the mission. So without McCoy there, Kirk might not have come to his senses.
Which is why Kirk wanted McCoy there in the first place. He knew McCoy would tell him what he needed to know rather than what he wanted to hear. One thing I've always found interesting is McCoy's about-face regarding Kirk needing to captain a starship. He told Kirk that he was obsessed with the Enterprise in TMP but later encouraged him to get his command back. I suppose McCoy had plenty of time reflect during the years between TMP and TWOK and realized that Kirk was meant for starship command rather than the admiralty, something Spock also recognized.
--Sran