Like you said, they went overboard with it. A far more suitable way would be just to have Kirk violating the Prime Directive to rescue people who would have died. That would have been a better characterization of Kirk, someone willing to ignore the rules to do what he believes is right as opposed to the bad boy punk who doesn't believe rules should apply to him.
Well, violating the Prime Directive is something that Kirk never outgrew. Kirk Prime was doing it all the time. So to give Kirk that coming-of-age story arc, his immaturity had to go beyond just breaking the Prime Directive.
But yes, we're in agreement that they went overboard with the immaturity angle in the early part of STID. I mean, Kirk hardly does anything right in the first third of the film.
Having said that, I'm very glad that the writers tried to give Kirk a strong story arc, and the whole coming-of-age angle was a good one for him. I also don't blame Pine at all, as I think he did a really great job with what he was given. It was just...the writers laid it on a bit too thick at the beginning.