There are other possibilities like bad writing or the screenwriters' racism. Sulu should have been in command as the highest-ranking officer after Kirk and Spock. Even during the show, Sulu was never left in command of the Bridge when Kirk and Spock were on an Away mission. Instead, Scotty was left in charge. Although a higher rank than Sulu, he was not a Bridge officer.
You've already been shown you were wrong about Sulu never taking command in TOS...
So, just to be clear, those same racist screenwriters who wanted to keep Sulu out of the captain's chair are also progressive feminists who wanted to give a prominent role to an independent by-the-book professional woman who advances based on her competence and intelligence?
Those same racist screenwriters who also originally scripted that Sulu would be taking command of the Excelsior in a few weeks time wanted to keep him out of the command chair?
The same director who did give Sulu his own command (as was originally intended) in his next Star Trek film wouldn't override that racism given the enormous amount of influence he had on the tone, production design, story, etc.? I mean, he made his movies into nautical themed or Holmesian whodunnit yarns with actual pots and pans and formal wraparound uniforms but he couldn't say "hey, let's put Sulu in the big chair"?
Or could it be, they wanted to juxtapose these old(er) mostly men and the theme of aging with a young woman (and to a lesser extent a young man in David) who had as prominent a role in the film as they did?
Could it be that Kirk expressed concern about cadets at the helm and was visibly nervous at a cadet piloting the Enterprise out of spacedock, so maybe having an experienced officer and a steady hand at the helm rather than barking out orders from the captain's chair is more important, especially since he's literally five feet away and the ranking officer if shit got real?
But no, let's just baselessly accuse people of racism, because that's not an ugly thing to just casually accuse someone of without evidence.