The Internet isn't controlled now by the US, government or otherwise. ICANN happens to exist as an entity in the US, but its board of directors is very international. In fact, ICANN was created to remove control of the Internet from the US government. So, basically, your premise is completely wrong.

In addition, the Internet works as a result of cooperation, not as a result of mandate. We can all choose different DNS root servers now if we wanted to. There have been a number of alternate DNS roots in the past and they've never worked out. ICANN would have to give up its control voluntarily or, maybe, every network provider would have to block them from existance. I don't see either of those happening, so I don't see it as an issue regardless of your premise.