There is plenty of evidence in the films to suggest that they were in fact moving on with their careers and off the Enterprise. In TWOK, Chekov is XO on Reliant, and Kirk's line about having Sulu "at the helm for three weeks" suggests that the Ent is not his regular posting. Having everyone on the Ent-A in TFF is easily explained by all of their careers suffering some fallout from the events of TSFS. In TUC, Uhura references chairing a seminar at the Academy, McCoy wonders if they are being thrown a retirement party etc. Sulu has been in command of Excelsior for a number of years at that point also.
The only clear time in the films that all of our principals seemed to be permanently assigned to the Enterprise are in TMP, TFF, and TUC. TUC is clearly stated to be the last mission for that group on the ship.