It isn't just about nukes being pointed at each other either. War is far more expensive than cooperation, even if you disregard the 'cost' of human life.
Pardon me, but I think I responded to your points in a detailed and explicit manner. I even provided support evidence through external links. You have yet to provide links, nor bother to refer to mine.
Credit scoring is ostracism in a group of more than 150. As is ex-communication in the Catholic church. Ebay uses ostracism in its ratings system, as do many other sites which form any form of ratings system. There are many other examples. If your 'decent body of research' refutes this, let's see it.
Incidentally, credit scoring transcends borders, as does religion and the Internet in general.
I assert that arbitration can work of any parties of any size. The parties who are not being judged (ie. everyone else) decides how much influence arbitration has, by deciding how much they respect the judgement. Where is your evidence to the contrary?
If one big organisation owns a bunch of courts, it doesn't mean that they will be respected. If they use them unfairly, it will just lead them to having a bunch of courts which no one trusts or cares about.
Even if the cost of war was 'cheap' (very unlikely), do you think everyone will just stand idly by, still using said organisation's services? Of course they wouldn't - they would call it inhumane, violent and shameful, then ostracise them, cutting off their income stream. Empire building just isn't seen as morally acceptable any more, even by nations who are wealthy enough to do it (arguably, the gap between rich and poor countries is too small to exploit too).
If such an organisation didn't care and wanted to wage war on the people by threatening them and stealing their stuff, then people would work to overthrow them. The state only functions now because most people are happy to submit to it. This wouldn't be the case where being ruled was seen as a violation of individual liberties (which seems to be where things are heading, IMO).
The whole of human history proves you wrong.