i'm jumping in too...
I think it's relative unrealistic...but again "It's only a TV show" (or in this case, movie). So we'd need a number of excuses to push Kirk into a place where he's best qualified.
1. He knows the ship better than almost anyone. Pike said that Kirk's test scores were off the charts (i.e. smart). He lived near the shipyard. So he might hav emade friends among the workers, and learned what was going on, maybe hear of whatever special changes were made, etc. Also since, he wasn't attached any part (like the crew making the warp engine, the crew building the sick bay), he wasn't tied into the cliques that often form (and thus not share info), and could connect the different aspects fo the ship in his mind. He'd be like Will Decker of TMP.
2. He knows the crew better than anyone. Again, he lived near the shipyard, and as we see from his first encounter with Uhura, future crew members visted the area (if not live there for a short period). Despite the fight he started, he might have met others, and already earned their respect (maybe help them with a class project, give them a pep talk, etc.). Over the several years that Enterprise was being built, different personnel might come at different points (such as to supervise a system being built), then re-assigned for stints on other ships if they weren't going back to the Academy. Kirk would have bene one fo the few constants, and while the crew members missed each other, he would have known nearly all of them at some point.
3. He had outside "college credit". Since Kirk was a bit older, it's probable he went to college already, and had taken courses that could be transferred in, allowing him to do things like take advanced classes that a command officer would take. (Assuming Starfleet Academy was a type of college...Kirk could have been taking graduate level classes that potential Captains might have taken later on in their career)
4. He had outside/extra experience. Kirk might have been in space already during his pre-Academy days, even "commanded" a ship of some sort, or did something that people could look at later and say (oh yeah, he's a leader), like lead some rescue. During his Academy days, because he had the aforementioned credits, was able to take a semester and/or summer to spend it on a starship. If there was a scenario like DS9's "The Valiant", his brief command experience would be on record.
5. The Academy had already "command tracked" him. (Please forgive the follwoing -- but just too give some "logic") From my days with the fan group Starfleet Command, graduating from the Academy already made you an officer -- Ensign. From what we saw in TWOK, it seems like the best graduates might be able to prove themselves enough to straightaway become a LT junior grade, or even a full LT. Perhaps even the best of the best might qualify for LT Commander, or at least shorten the length of time they needed to stay as a LT before promotion. So Kirk was the best of the best in his class (disregarding behavior)
6. Not enough command officers. With the Romulan attack, perhaps some of the more experienced, command-track officers joined existing crew complements, to shore them up and make sure they could take care of them enemy. (Kinda like what we see in TWOK -- in a sense) Unfortunately, they perished. Those that outrank Kirk that wer eleft may not have been the best choices for overall command of a ship. They might have been a great Chief Engineer or Chief COmmunications Officer, but they wouldn't make a great overall comman officer (i.e. they are stuck in their 'box").
7. Admiral Pike. Surely Pike had A LOT of credibility with the top brass, just by himself. But how much more so when it's revealed that's he's the one who recruited Kirk, the savior of the Federation, it's obvious Pike has good judgment. And since Pike (apparently) can't serve on the Enterprise anymore, he feels like Kirk earned the trust Pike placed in him way back when. So Pike feels most comfortable handing over his "baby" to the man who brought the ship, and the Federation, from the brink of destruction. The only other person would have been Spock, who Pike might know to be better suited as First Officer. And in "the real world", politicians and comapny managers often hire "friends and family" so underqualified people get positons ahead of the more qualified.
I too would have liked a "3 years later" type of deal where Kirk has had a chance to earn his stripes.
But it might make a good story if some of his crew has the same doubts we express, and Kirk wins them over by some great command decisions. (Maybe have Ben Finney character express that -- but without the TOS episode story line)
It's a fun read, and the nice thing about successive volumes is that the author fesses up to mistakes from previous volumes or nits that he missed even with multiple viewings.
