Decker was supervising the refit, and the refit starship was launched prematurely. I don't believe that there's anything we're shown on screen that would tell us whether Decker would have captained the new starship beyond her shakedown cruise. The conflict we see is between the egos of Decker and Kirk, where the argument that Decker has against Kirk is essentially that Kirk cannot qualify in time regarding the capabilities of the ship that are new and different from what they were in the version of the ship that Kirk had captained.
I'll also add that Kirk arguably was performing at least part of his function in Starfleet by replacing Decker. The self-gratifying aspect of replacing Decker with himself was how it got problematic. What would have made it seem less selfish would have been a line or two about there being no one who could get there in time who was more qualified than Kirk to make first contact with aliens posing an existential threat to humanity. This is precisely the sort of thing that could have been said in the conversation between Kirk and Admiral Nogura.