The humans still control the resources and determine the course of events, somehow, and use the universe mostly for their own purposes.
Or at least, the society made up of humans plus many AI minds much smarter than humans still has feedback systems that make it stably want and do what is actually best for the humans. I.e. the structure and enforcement mechanisms of the society ensures the ASI consensus is humanitarian. This requires the goals structure of the ASIs to have some rather different properties than many forms of goal-maximization would produce.
Or at least, the society made up of humans plus many AI minds much smarter than humans still has feedback systems that make it stably want and do what is actually best for the humans. I.e. the structure and enforcement mechanisms of the society ensures the ASI consensus is humanitarian. This requires the goals structure of the ASIs to have some rather different properties than many forms of goal-maximization would produce.