The idea of McCoy going to Starfleet Academy has been used in many novels from the 80's and 90's. I believe Dr. Crusher went to SFA too. They wouldn't just pluck a doctor from medical school and put them on a starship - they'd need training in starship procedures, protocol and non-human medicine.
But a another four year school? Like was stated upthread... many things taught at the Academy would be redundant for a college graduate.
About 17-year-old Ensign Chekov, Wrath of Khan's cadet Peter Preston (Scotty's nephew, who died during Khan's first attack) was supposed to be 14(!), but the lines mentioning it were cut (along with Saavik being half-Romulan).
The whole Peter Preston being 14 made no sense. It's not just about how smart you are, but also maturity. The kid was barely high school age. I tend to give Chekov a pass.
The idea of Starfleet in STXI was that if you have a gift, you will be given a chance to use it to the fullest.
Actually, the only thing I got from Star Trek 2009 was that 'rules are for losers'. I think its' important for Star Trek 2012 to show the flip side of the coin. What can go horribly wrong when you don't follow the rules.