The Internet is not controlled by the U.S. or any other country. If all U.S. links are severed tomorrow, the Internet will still exist: there will still be interconnected networks, and packets will go through.
The root zone of the domain name system is controlled by the U.S. But, handing over control from one organization—the U.S.—to another—multinational agency—is not a solution. The real solution is decentralization: abolish Net-wide root zone altogether, and manage the namespace competitvely, recognizing country top-level domains by agreement. (The obvious question is, how do you introduce new global TLDs such as ".xxx" then? The answer is, you don't. Stay tuned for a discussion of why new generic top-level domains are not needed.)
Can you expect the U.N. to start a revolution?