The real No. 1 should be in the 2009 movie how Kirk gets promoted to Captain straight from Ensign as a reward for repeatedly breaking the rules. There's no rational reason for this to occur at all, but it does. It also annoyed me that instead of the movie just being a self-contained reboot, a ton of the backstory was essentially offscreen schenanigans.
AFAIK, it's navy tradition that whoever is in command of a ship has the exclusive use of "Captain" or "the Captain" (in addition to their regular titles).
Like at the start of Star Trek II, Admiral Kirk was a guest on an Enterprise commanded by Captain Spock, so Spock could be called either "Captain" or "Captain Spock". But then he gave his command to Kirk, so Admiral Kirk became "the Captain" and could be called "Captain" or "Admiral" or "Admiral Kirk". And it became improper to casually refer to Spock as "Captain" even though he was one.
I haven't seen Star Trek 2009 in a while, but I don't think Captain Pike actually promoted Spock when he left the ship and gave him command. He merely gave Spock non-temporary command, which automatically made him "Captain", and he gave Ensign Kirk the position of first officer, even though there were others with higher rank.
When Ensign Kirk (using his position as first officer) removed Spock and took command, he automatically became "Captain" but I think it would've still been okay for people to call him Ensign or Ensign Kirk.
Official promotions would have been handed out at the awards ceremony at the end of the movie. At which point, yeah, they probably officially jumped Kirk from Ensign to Captain and let him keep Enterprise instead of giving it to another more qualified Captain and giving Kirk something less valuable, which would've been really dumb but that's Hollywood.
Also: Vulcans. Enterprise (the TV show) says the twisted meritocracy they pushed on Humans likes to give things to the people who want them the loudest.