"So could it be that not all Connies have virtually the same compliment? Could some crew rosters differ depending on assignment/mission profile?"
"All these people" are needed for other, very practical reasons. The Enterprise
occasionally will leave a small group of people behind on some planet, for a variety of reasons. ... It dictates a crew complement large enough to withstand those temporary losses of personnel and still continue normal operations. (Making of Star Trek,
part II, chapter 3)
P.S. Connies? Are you talking about the class the movie Enterprise
is a member of or the original Enterprise Class the TV Enterprise