Their authority ranges across borders. They propagate and enforce regulations that apply in all jurisdictions. For instance, representativeness. Another difficult issue involves challenges to authority. It's difficult to maintain governmental authority if parties dissatisfied with the outcome can turn to another venue.
Accountability is also tricky.
The question is difficult to answer. At present, the Commerce Department's National Telecommunications and Information Administration exercises at least a supervisory role. America's dominance of the early days of Internet governance was a natural consequence of its seminal role in the Internet's creation. These concerns are expressed now in theoretical terms. The symbolic recognition provides a small reminder that organizations to which significant authority is delegated have a funny habit of using it in ways that few imagine.