One has to wonder what aspects of artificial intelligence would be needed for controlling a Starfleet ship, or assisting in controlling one. Would the AI have to be capable of fluent colloquial speech, for example? Of expressing emotions or cracking jokes? Or could it be all business and speak in a monotone voice?
It would seem likely in light of "Tomorrow is Yesterday" that a starship computer is trivially capable of passing the Turning test, and is prevented from doing so simply because Starfleet hates computers that talk back. The "I'm sooo humanlike" routine is simply turned off as default, but can be brought to play at any time - either in specialist subprograms being run by the computer (such as holoentertainment or expert programs), or in the main interface of the computer system.
As far as the Prometheus
is concerned, we could argue it's a sign of Starfleet not trusting robotic ships with combat after all. While the vessel seemingly flies with just four live crew (and can be flown with zero), its one known crewed section is stated to feature seven decks between Bridge and Sickbay, an arrangement that would make no sense if the four crew on the four Bridge seats were the intended operational norm. Quite possibly, the two combat sections with the big warp engines are drones - but rather than being fully autonomous, they are slaved to a rather heavily crewed control section, in a compromise that eliminates some of the downsides of the M-5 disaster while playing up the advantages.