I don’t see any necessary correlation between centralisation and cooperative behaviour.
All large scale cooperation requires is two sets of things:
1/ universal respect for individual life and individual liberty (which means responsible action in ecological and social contexts, and acceptance of expanding diversity); and
2/ sets of attendant strategies to detect and remove exploitation by cheating strategies.
So while I am all in favour of global scale cooperation, I see any sort of global centralisation of systems as a major source of existential risk.
Thus I favour distributed cooperation, at many different scales.