3. Cadet to Captain? - True, but it's a super hero origin story. Kirk saved the earth with that crew and that ship and in that logic it works, in the real world..... of course not. As much is Trek is a look at what could be, it is still really, really fake.
Kirk isn't a superhero, and Star Trek has never been a superhero story. And even within the logic of a superhero story, it still doesn't work for me. Especially not since they went out of their way to start Kirk not only as a cadet, but as a cadet on academic suspension.
I almost got hopeful at the beginning of STID that the entire thing was actually intended to be unbelievable, so it could open up some serious story possibilities about Kirk's leadership, but then Pike is murdered and the entire thing is completely forgotten again.