The real question is why Uhura never made captain.
I could well imagine she made Captain and then later Admiral, I doubt she would have ended up commanding a ship though as I could see her more at home working at SF Command or the Academy, there are many posts a Starfleet Captain can take up other than sitting in the centre seat of a starship.
Scotty never wore command colors despite being promoted to captain, though his rank was more reflective of his expertise and experience than any sort of command authority. He was second officer during the five-year mission but spent the rest of his Enterprise tour almost exclusively in engineering, only coming to the bridge for urgent repairs or to speak with Kirk directly.
Scotty was an odd in the later films, he actually wore both Engineering and Command colours, Engineering gold/mustard when he was in full uniform and then the white undershirt of a Captain when at work on the Enterprise with the black utility vest.
As for Chekov, he was obviously competent enough for Kirk and Spock to leave in command in V and VI as he was seen a couple of times in the Captains Chair. I always liked the idea he would have been Sulu's XO after the events of TUC and later made Captain even if he didnt command a ship.