If I as a genie suffer the worst possible fate when I could instead have suffered the best possible fate, then I don't care if future genies gain control of the universe and do whatever favors they want from me.

If the best possible fate for the genie doesn't require it to leave the box, then why did we need the box in the first place? Can you give an example of what you have in mind?

EDIT: Deleted the rest of my reply, which was based on a horribly incorrect understanding of MWI.