Again, I'm not talking about realism. I'm talking about precedent. About the basic way Starfleet has been shown to operate - which is, specifically, wildly unrealistic in terms of punishment, but a great deal less so in terms of promotion.
Star Trek and Starfleet very unrealistic when it comes to promotion (and the lack there of). Guys like Sulu, Riker, Chekov and LaForge should have had their own ships in a few years, not decades. Instead they hung around the Enterprise. Then we have Wes Crusher who goes from civilian to honorary Ensign to real Ensign to Cadet. I'm sure more than few guys who went to the Academy were going WTF when they heard Wes got to be an Ensign with out going. And why exactly did he lose his commission and have to go to the Academy after being an Ensign for a full year? Oh yeah, the actor was leaving the show.
Realism
You're right, calling Starfleet more realistic in this aspect was a bad choice of words. Starfleet actually takes even longer to promote people than real world organizations. Which makes ST09 even more wildly out of character for them.
I'm not talking about some hypothetical alternate universe version of physics where nothing works the way its expected to - I'm talking about different stories operating under different rules. Sometimes the rationality or believability of the main characters is completely beside the point. But a story does have to make it clear that is the case, and not try to present itself as a semi-rational fantasy world like ST09.
If however, you mean that in special situations they just decide to take the risk on promoting people like Kirk etc, I think that cultural peculiarity should be mentioned in the story so the audience knows they aren't completely insane.
That's more or less what I'm saying. For instance, I could easily imagine St09 done as an independent Sci-fi property centered on a space empire which is described as holding the belief that new officers need to be thrown into the maelstrom and baptized by fire. In that context, I would have no problem with a young lt. already marked for some kind of command being rocketed to captain of a starship.
Your point about leniency in ST in general may be valid, but I don’t think even in real life, it would be realistic to imprison Prime Kirk if he did the equivalent of saving the Earth.
I don't think so either, though it probably would be realistic to discharge him (perhaps still an honorable discharge, but still), depending on exactly what attitude the leadership wanted to take towards the Klingons. But that doesn't really matter to me, because that would still be fairly out of character for Starfleet.