The DNS has to stay being controled by one or more democratic countries. As much as I like international organizations within the UN framework, but giving control of the DNS to a UN committee would make it too easy for China to just give a number of poor countries some more money to by their votes for whatever China wants to see banned from the net. Not paranoia, that is common practice, Western countries are doing it too. But at least Western governments are controlled by their populations to some extent.
Why does it have to be controlled by anyone? If you mean to keeping the existing infrastructure as-is sure, but I think that's not such a great idea anyway.