You're right, they wouldn't have to be teenagers. Depending on their species (when they mature) and their history, the Academy would admit cadets from two Earth years up to 200 and beyond, which would help add a bit of diversity as well.
Commander Austin Harris, First Officer, Deep Space Nine (by FltCpt. Bossco)
8.01 - Darkest Before Dawn
(Chapter 8 added, 12/09/2015)