Yes, because everything else the US controls has been so hunky-dory in terms of freedom and transparency. It doesn't matter who controls ICANN, it will never be 100% fair. People aren't fair. Just because the UN is a giant spin agency to cover up atrocities and foreign corruption doesn't make the US any less evil by default. You're looking at it from the wrong perspective.
What ICANN should be is a system designed to be as open as possible, and if certain networks object, they can censor it themselves as is already done. The issue of Saudi Arabia being an unenlightened medieval shithole of theocratic sociopaths has nothing to do with converting letters to numbers on the internet. Let ICANN worry about the internet, and let the warmongers figure out who's right and wrong in the world.