It's not any individual society that "doesn't work", per se. It's the interaction between different societies and the inability to accept or negotiate common ground that is at the root of the problems occuring globally. And that boils down to respect for those that one does not understand.

In my opinion, an all Atheist world would be no different from a world inhabited by all Christians/Muslims/Hindus or members of the Church of Fire and Brimstone and God's Almighty Baptizing Wind. It's not without problems, but generally much easier to get along if all think alike.