But I don't think that's how it works at all. Things are stable when people believe they are stable, that's it. Just like speculative prices in markets. Communism and socialism sort of worked for the short stretches of time that people were true believers in them - imo it failed bc it contradicted human psychology so the belief couldn't last. Capitalism is stable bc people believe in it, probably bc it matches better our competitive and aggressive psychology.
If the Overton-window shifts to a place where people can start believing that "global orgs" can be stable, they will be stable. Maybe it's more complicated, maybe that place is pretty strange and far away. But I wouldn't think so, it's only needed that one proof-of-concept implementation starts to be believed as stable and beneficial, and then the pattern can be propagated through a chain reaction of people betting more and more on it and then fighting to protect the outcome they've betted on.
Think the French Revolution and the ensuing toppling of most monarchies throughout Europe - that's probably the best model we have for a process like this, just that instead of toppling you'd hopefully have transformation (think modern parliamentary monarchies like the UK, which successfully transformed), and it worked out for the better in the end :)