I am a firm beleiver in star fleet is big. Space is vast and to defend so many member worlds would take a big star fleet. Now I bet star fleet does have a large number of ships in mothball and only activated during the time of war.
now when it comes to star fleet academy I've always figured it was just the "elite" university. One of many places cadets go(and this is for officers others go to the various other boot camps or other places)