Bur realistically though it'll be just an awful lot of gratuitous harrassment by every piece of shit in the world that is hostile to the U.S. and got no balls to beat it militarily, or culturally, or economically. Mostly at the US's own expense, btw.
You know very well from our everyday life, w/o any international issues involved, that simply to be taken to court is a bunch of trouble: even if you win, or can win, or the case is unjustified, or whatever. The simple expense and other costs (time, human effort) of litigation is frequently enough to punish the innocent. For example, say a big corporation with deep pockets takes you to court, and suppose their case is week and they probably can't win outright -- so what? They still can inflict enough damange on you w/o winning, cuz you got no comparable money and time and may even be wiped out even if they don't win, or even before this can be decided. That's why cases are frequently settled out of court -- just to minimize losses, regardless of who's right and wrong.
Now make that international, where the stakes are not some patent infringement, but political control over significan't chunks of the earth surface. 'course it's bound to be self-defeating for the U.S. to expose itself in such a way to a horde of petty evildoers.