Gene Roddenberry's "Andromeda" tackled this pretty well I think. The warship can be operated pretty much entirely by the on-board sentient AI, and it is because it has a skeleton crew of like 6 for most of the series. Because the AI is sentient, every commonwealth ship has a personality, the ship itself is a person.

It also has storylines that explain why AIs don't literally run everything: there was a large lash back against the proliferation of AI after the fall of the government, to the point that there are planets that completely ban their existence and destroy on sight.