Trek 09 has the scene with Kirk getting taken to task over cheating, but we don't know if all the cadets in that auditorium are A) the entire student body of the school, B) all the students in Kirk's year C) any other random grouping of students.
If starfleet were truely large, even huge, in terms of personnel, then the people we see there could just be the ones in Kirk's form or class of cadet. One of their own stands accused, and they're all required to be in attendance. There looks to be around a thousand people in the seats.
If starfleet academy is a four year institution, and they graduated one class a month (48 separate classes on campus at a time), and there is a ten percent wash-out rate, they would graduate and commission approximately eleven thousand new officers per year.
That would replace officers retiring, resigning, discharges and dying each year. Plus any expansion on starfleet's part.