In the vast majority of interactions, nobody sues anybody. Why does a monopoly make the thing more efficient? In any example ever found in history, a monopoly has resulted in worse services at higher prices.
Case in point: What about international business transactions? How would you get a foreign client to pick, let alone trust, one of many private court systems?
Multi-national corporations are essentially anarchistic already. They operate in countries in which practically anything goes, or in which bribery is a part of doing business. They employ experts in various local laws, but as long as they're careful where and how they do things, they can do practically anything they want.
Not that I'm entirely in favor of that. But to suggest that government somehow makes international business easier, cleaner or more orderly, is almost funny.