The answer to the question "Who believes UN governance will result in improvement?" will give a lot of insight into the motives behind transferring control to a UN agency. My immediate suspicions include: the copyright cartels, repressive governments, and telecoms/tier 1's seeking to create international monopolies
How about citizens from the rest of the world who would like the Internet controlled by a body that we actually have some say in?
I mean, just take Europeans, Canadians, Australians, New Zealanders, Japanese, Koreans. This sub-group of Internet users collectively outnumber US citizens by a large number. They all add a lot to the Internet. Why should they be dictated to by the US? Why should they be denied a voice in how the most important technology of our age (which is of vital importance to modern business) is run?