Yes, this is certainly the biggest hole in the film and the hardest to wave away, even for someone who loved it as much as I. Kirk was known to have been (at the time) the youngest Captain in the fleet, but the writers made a mockery of this fact.
It was natural that Pike would name Spock acting Captain (he already held the rank of Commander and was presumably XO already) but after Spock you'd have expected the existing chain of command to be followed. (A small comment on this is that McCoy's line about Enterprise having no captain and no first officer to replace him, if it made for a good dramatic line, was unnecessary and illogical in light of the above fact). Ummm, there WAS a chain of command, right? If there was one the crew trampled all over it!
Contrived to say the least to make Kirk the hero he was "meant" to be - a little like taking a good plot on the whole but trying to squeeze cadet Kirk in as a square peg into a round hole.
"If you can't take a little bloody nose, maybe you ought to go back home and crawl under your bed. It's not safe out here. It's wonderous, with treasures to satiate desires both subtle and gross... but it's not for the timid." Q, Q Who