I really don't care about the "cadet to captain" complains I mean really using that logic we should have a trilogy of movies about Bruce Wayne where he doesn't become Batman until the tail end of the last movie.
Going from cadet to captain was a real problem for me as it was completely unbelievable. You have Kirk taking command when everyone else on the bridge outranks him. They could have all the Kirk and Spock conflict by having them both be lieutenants who are unsure how to proceed once they loose the captain and first officer. Going from lieutenant to captain would have at least been more plausible.