I don't think the world needs a strong government. I think the world needs to ease up on economic globalization, precisely because it cannot have (and should not have, for reasons you discuss as well) world government. Once you accept that political authority needs to be fragmented, you have to live with the economic transaction costs that this brings, and not assume you can wish them away.
My point about Europe was that I thought this was the only region in the world that could/should potentially move toward closer political integration. Recent events have shown that they too have no other option than easing up on economic union.
At the risk of misinterpreting Rodrik again, I now see him as asking under what conditions there can be uncontrolled capital flows without creating economic disruption. So, within an optimal currency area (where labor is fairly mobile), the market can handle large capital flows across regions. Another way of saying this is that if we do not have separate nation-states, we can handle capital flows.
He also suggests that if individual states are not subject to democratic pressures, then we can have globalization. The 19th-century gold standard is his example.
I guess my hope would be that we could have international capital flows, in spite of linguistic differences and other barriers to labor mobility. I have issues with democracy, but let's leave that in the mix for now.
The disruptive capital flows seem to consist of the biggest banks herding into particular countries, then screaming for bailouts when something goes wrong. The conventional wisdom, now as always, is that the bailouts are wise.
I think of the bailouts as the equivalent of paying ransom to kidnappers. It doesn't solve your kidnapping problem.
The way I see it, the heart of the challenge is the symbiotic relationship between Big Government and Big Finance. If one or the other--or both--were to go away, then I think large capital flows and globalization might not be so hard to deal with. If both Big Government and Big Finance are immovable, then I can see where globalization is going to get ugly.
It is not the role of the ECB, IMF, or Federal Reserve to bail out banks. These measures are profoundly unpopular with voters in countries such as Germany and the United States. I think it is incumbent on the architects of these measures to communicate what is the structural defect in banking regulation that made such intervention necessary, and what reforms have been implemented to ensure that such measures won't be needed again.