Fridge Logic: Why are cadets engaging in combat on the front lines? Well, they're usually not. With a few exceptions, most of the action seen on the show is actually on minor fronts, a way for the cadets to get experience without getting killed in the important battles, not to mention a way for the troublesome Commodore Tolwyn to be put to productive use.
It also harkens back to the Age Of Sail, where it was common for cadets (typically called Midshipmen in the American and British navies) to receive their training by serving aboard a sailing ship and essentially learning on the job. Hence the prevalence of the Plucky Middie in fiction taking place in the era. The practice was eventually phased out (along with similar practices for enlisted sailors) in favor of professional training programs offered on dry land.