As far as Kirk's advancement in Starfleet in the JJverse, I pose this: Kirk is a genius. Kirk is a natural leader. He's the 'Good Will Hunting' of Star Trek. End of story.
Cadet Wesley Crusher promoted to Captain is believable to?????????
Well, not much about Kirk, Starfleet or Star Trek
has ever been believable in real world terms.
I don't know why fans have decided that the reboot was a good time to notice that and start complaining.
The idea of a man Kirk's age being in command of that ship was always preposterous, something that the producers
were fully aware of - they noted in the writer's guide that he was the youngest to have such a command and that therefore a "legend" was growing up about him. Every other captain of such a vessel that we saw in either TOS or TNG was greying and a decade or more older thank Kirk, save one - Tryla Scott in "Conspiracy," and again a point was made that she was extraordinarily young for the job.
The only standards by which Abrams's version of Star Trek
falls short of oldTrek in terms of plausibility or real scientific accuracy is if one uses oldTrek as the standard - ie, "to the extent that this is different from TOS or unfamiliar, it's wrong." If one uses any kind of reference to reality or even unbiased logic, both fall really short.