What about Dr. Piper and Lee Kelso? And why are women wearing skirts instead of pants... And why doesn't the bridge have the "war of the worlds" microphones coming up from each station? Why are they using the color red in the uniforms? etc... etc...
Look,
You cannot possible make a movie that is supposed to be a reboot/update of TOS, if you insist that everything is held hostage to the characters and events of one episode, especually a pilot episode.
This movie is trying to introduce 7 new actors to play the biggest 7 characters of TOS. How confusing would it be to a casual Trek fan, or a non-Trek fan to have a movie that prominently featured a character they probably never heard of? And all of this in an attempt to satisfy a group of "fans" who will a) never be satisfied and b) will definitely go see the movie anyway, if for no other reason than so they can bitch about it.
Having said all of that, a brief reference to Mitchell and/or Finnigan, that doesn't really impact the story either way, would be a nice nod to old time fans.