If it was SO different though why would you have so many of the original crew still serving together? I mean why would Spock or Scotty or even Uhura be serving on an Enterprise run by Kirk rather than be on another Starship or even different career or they could have been dead? I know it's only a 50 minute television story as well...

JB
I believe that in each visit to a Mirror Universe, that MU is
created all at once by some precipitating event (like the ion storm in "Mirror, Mirror"). The MU had no prior existence; it came into being suddenly and imperfectly like a bad Xerox copy. So all the same individuals are copied into the MU, and in
similar relationships and proximity, but they are different as well.
The created MU might then continue to exist after the Prime Universe characters leave it, or it might vanish. The science is not settled on this point. I believe it vanishes due to the Law of Conservation.
Granted, I have to disregard DS9's very decent MU episodes as fiction, maybe short stories by Jake Sisko, to make the math work out. This also explains how Vic Fontaine could be flesh and blood in the DS9 MU -- because there is no DS9 MU.