I saw this the first weekend, like many others. And it was in an IMAX theater. I don't think I've had that experience recently, and when the first trailer played I thought "oh, wow, what a sound system."
Star Trek was the long waited reboot of the Star Trek series, from the original. And its notable because of the youth of the characters. In particular, while Spock and Scotty have some level of experience (and McCoy is still a doctor which is a different track), Kirk, Uhura, Sulu, and Chekov are fresh out of training (or abbreviated training in the case of Kirk).
While I imagine there is the idea of an appeal to youth, the crew relationship and development is one I tend to react rather negatively too. To make a point of it, it depicts an environment where success is due to chance and turn of events, and not decision making. While thrilling, to me it is unsatisfying.
A very strong counterexample is the remade Battlestar Galactica. There you have a crew made of senior and junior officers and enlisted men. And amidst all of the pressures of war and imminent death as a consequence of failure there is a dedication to each other, mentoring between senior and junior, with seniors making decisions based on wisdom and experience, and purposely guiding the junior personnel so they may also grow in wisdom and experience of their own. And in the original series you saw it as well. By the time Kirk is captain, his backstory includes a pattern of development and mentorship and experiences. The movies have it with Decker and Sulu being protoges of Kirk. Scotty's nephew, Spock's mentoring Saavik and Valaris. With our new Captain Kirk, there is no sign of any development of the person, only raw intuition and emotion. No development of leadership skills, empathy, instillment of loyalty. It shows in the Kobayashi Moru scenes where his fellow cadets follow his orders in a bored offhand way instead of the crispness that they have been trained, even if they viewed his orders as silly (after all, they are being evaluated too). And no indication that Kirk cares about the development of anyone around him (other then checking that they appreciate and recognize his moments of brilliance.)
But would someone follow such a person? By the end of the movie, Kirk has good moments. But in many ways he was merely lucky many times, and he does not show the ability to work with people that marks the other captains in the movie, or the other captains in the other Star Trek movies and series. There is a saying that you'd rather be lucky then good, but would a crew be inspired to work by such a person?