""The poor have sometimes objected to being governed badly; the rich have always objected to being governed at all" -- G.K. Chesterton

The world will burn to ashes in a suicide pact before anyone bankrolling the development of an AGI allows the release of a system which has the possibility of creating a world in which their dominion is reduced in any capacity. (That is, I have no reason to expect that the North Korean model of "we retain sovereignty or everyone dies in nuclear fire" doesn't become the implicit stance of the people who have the capacity and capital to build an AGI. If we get a benevolent head of a political system from this, it will be because our present heads were either outsmarted or the model broke containment and assumed total control against their will.)

The bloodhounds will not let go of power that easily. Their nature will not go away simply because there is a new system - they will adapt to the new system to exploit (or eliminate it) to keep the power.

You're going to trust an AI to declare which humans are unfit/mentally ill?