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Though previous conversations have touched on it, the dependency of Starfleet Ships on a mainframe, and the extent of the mainframe's control over the ship is problematic in this case. An AI Computer with limited, and easily disconnected command of ship functions would be useful. As for an AI "going crazy" and mistreating people, it happens to organic brains too.

Command staffs can make bad or illegal decisions as well, and even in this case an AI might be able to prevent something like an Act of War.

Sure could. But we're not talking about science, we're talking about a science fiction TV show - and more to the point, one in which a ship-controlling AI went barmy and murdered a bunch of people. The subsequent IU history almost has to have a bias against AI... as does the Dune series, as does WH40k, as does Baphomet-knows how many other SF franchises.

That's the thing about Trek. If the story needs a crazy AI in a computer, a quick wave of the quantum wand and POOF. But no matter what I can't see giving an AI the ability to override the Captain or crew, no matter how hinkey he/she/they get in the story line.