Human cultural evolution has already created self-proclaimed "perfect" cultures that went on to attempt exactly this. The Nazis were only the most recent notable example. There are many examples in history of groups who considered it their holy duty or moral duty to take over the world. Fortunately, for most of human history, this hasn't been feasible, but technology is changing this equation.
then the AI-human race will create a perfect society and branch off to explore the universe.
Physics tells us that the "speed of light" is actually the absolute speed of causality for mass-energy.
https://www.youtube.com/watch?v=msVuCEs8Ydo
So until consciousness can inhabit a substrate independent of mass-energy and based on space itself, and thus not subject to the light speed limit, any intelligent civilization which expands is doomed to create its own rivals. In Michael Swannick's Vacuum Flowers the Earth is taken over by a hegemonic super-intelligence, but it's forever trapped there, because when attempting to expand, the light-speed lag will cause a sub-part of it to bud off and immediately attack its greatest rival -- which is always the rest of itself.
In any case, civilizations are clearly not stable on cosmic time scales. Who in their right mind would think that billions of interacting sentients with their own agendas would produce any stable organization? It's ridiculous on the face of it.
http://www.newyorker.com/tech/elements/how-to-call-bullshit-...
> In the final chapter, Alex finds himself halfheartedly preparing for yet another night of crime with a new gang (Lenn, Rick, Bully). After a chance encounter with Pete, who has reformed and married, Alex finds himself taking less and less pleasure in acts of senseless violence. He begins contemplating giving up crime himself to become a productive member of society and start a family of his own, while reflecting on the notion that his own children will be just as destructive as he has been, if not more so.
Broadly speaking, the whole sentiment makes me uneasy, especially given how powerful a tool the internet can be for consensus building.
The latter makes it sound like a much worse version of ourselves.