The prime directive also prohibited the landing party from just beaming up or saying things like behold, I am the arch angel Gabriel. But how do you all feel about transporters on the bridge and an AI aboard the next show?
Candidly although the term is never used the ship's computer is already some form of A.I.
The problem with the perception of computer intelligence is that the bar is always being raised---your desktop computer or laptop is already a simple form of A.I. . I think the popular idea of A.I. is a self-aware, self-directing machine practically indistinguishable from how a human mind works. From that standpoint Data is an A.I. only in a humanoid form. But there are differing levels of awareness and differing levels of intelligence for computers just as there are for biological creatures.
How self-aware and intelligent is an ant, a dog, a cat, a dolphin, an ape, an octopus? They all have a level of self-awareness and intelligence suited to their nature and ability to survive. In varying measure they can operate independently.
As human beings we like to think we are eminently adaptable to new situations, and we are, but we still draw on past experience and knowledge to guide us. In a sense our past experiences and acquired knowledge are our programming. Yet we are able to bridge, to make new connections and think in the abstract to form variations on existing ideas. Can a machine be programmed in similar fashion?
A starship computer isn't simply a regulator of existing functions, but also has the ability to make autonomous adjustments without the need for human input. Actually we have that already in aircraft control systems, most particularly in advanced fighter aircraft that by design are inherently unstable to allow for high maneuverability. Numerous in-flight adjustments need to be made to keep the aircraft stable, far more than the pilot can execute on a constant basis for prolonged periods. A starship navigational computer system would need to be similar yet even far more advanced particularly at FTL speeds. There would also be other systems such as engineering and life support.
Kirk orders Sulu to enter standard orbit and Sulu inputs the command sequences, but the helm/navigational computer would autonomously and rapidly make all the necessary adjustments to execute the maneuver. Sulu is basically telling the ship to "go here" and the helm/navigational system makes it happen. The only variables are if Kirk wants a particular position or particular kind of orbit altitude.