We are not chimps. Our society does not resemble that of chimps.
Chimps don't go to work. They don't marry. They don't have mortgages. They don't have churches, or governments, or human rights, or school, or police forces. Chimps don't find themselves awake at 4am worrying about whether they can make next month's rent because a freelance client just dropped them.
I can perfectly well believe that lower-status chimps have more stress because they are attacked by higher-status chimps. But in my experience, the person most likely to attack me is not a successful startup entrepreneur, it's some drunk dude at 2am who didn't manage to pull.
I've been stressed and not stressed at different times in my life. Being CEO was pretty stressful. Being really poor was really stressful. Being comfortably employed and owning a house was probably the least stressful. There's not even any correlation with my status, let alone causation.
Why do we think that chimpanzee psychology has anything to do with human psychology? Do we have any evidence to support that? Saying that "we can prove evolutionary psychology conjectures about complex human behaviours because we can observe simple behaviour in chimps" is circular reasoning. The only thing we have in common with chimps is a relatively recent common evolutionary ancestor.