Need I remind everyone that the Enterprise in TWOK was full of cadets ("So much for the little training mission"), that the Enterprise recently refitted was the only ship in range in TMP outfitted with a new crew and untested systems. The fact that cadets were on these ships is a nod to these other movies.
People also seem to assume that the ship was populated only with cadets, which is unsubstantiated to say the least, as the comm officer on the Enterprise was a Lieutenant, whom Uhura, a cadet, relieved, and Spock, the first officer, was, well an officer, DUH, a Commander in fact.
Let's also not forget that it's a MOVIE.
There were nods and tropes in this movie that reference Star Trek movies and episodes in a multitudinous ways. To suggest, that this isn't a Star Trek movie is absurd and to suggest that Abrams and company just don't get it as absurd.