Starfleet has never actually claimed this, and it's pretty obvious that they DON'T. To begin with, the fact that Starfleet ORIGINATED from a non-military NASA-like organization in the first place and has no actual lineage to any navy anywhere, let alone the U.S. or British navies they have a tendency to imitate. So we don't actually know what it means to be an Admiral in Starfleet; it comes with rank, obviously, and probably a higher paycheck and the shifting of responsibilities from field work to desk job; it could, on the other hand, be an ELECTED position, and Kirk would only have gotten the job because nobody was running against him (Commodore Paris didn't want the job for some reason?)
Peter Principle: Officers continue to be promoted until they reach their level of incompetence, at which point they cease to be promoted because they are no longer capable of doing meaningful work.
I've always felt that Starfleet doesn't actually promote officers purely based on merit or experience, but that officers have to APPLY for promotion and have to actually prove they are qualified for their new position, like interviewing for a new job. This would explain 1) Why Harry Kim never got promoted (he simply didn't want to) and 2) why Spock was never given a command of his own (never applied for the position, and only promoted to "Captain" because it was required for his teaching position at the academy).
There are some holes in that theory of course, not least of which having to do with rank scale being tied with pay (like Morrow promoting Scotty to Captain is probably just his way of giving him a huge payraise) but it neatly solves the problem of "Hey, you're an excellent ace pilot, so now we're putting you in command of an aircraft carrier, with responsibilities that are totally alien to your skill set, because you're so awesome! Congratulations!"
Applying for a position and getting it are two different things. A paramedic with 20 years experience in a deep space colony could probably get the job faster than a 24 year old fresh out of med school who hasn't even finished his residency.
That's why I'm thinking it is probably based on an individualized assessment of aptitude, which Kirk would have to prove in order to take the position. He's obviously smart enough, arguably experienced enough, so nothing's stopping him from applying for the job. The only thing that would stop him from GETTING it is if someone more qualified applied for it, and it seems like the only person who fits the bill is Commodore Paris, who for whatever reason doesn't WANT the job.
