It sounds like a reasonable step. Insofar as the Internet is governed, it should be governed by an international body, right?
The problem with the analysis is that the Internet is not governed at all. Icann ensures that allocated domain names link to one unique site, in just the way that telephone numbers link to one, and only one, connection. It is a technical job. The fact that Icann is located in California and governed by US law is insignificant. Like Microsoft - also located in the US - it is accountable to its customers, not any government.
So why are some countries calling for a UN-sponsored body to take over the governance of the Internet? There are three main reasons.
First, policy makers in some dirigiste countries - France, most of the Arab world, some parts of Africa and, to a lesser extent India and China - genuinely don't get the concept of market accountability. Like all the anti-globalists they imagine sinister American conspiracies - many would add under Jewish influence - to control the Internet.
Second, some policy makers know full well that the Internet is not governed, and do not like this at all. China falls into this camp too, as does Saudi Arabia. The free flow of information is not something they want to encourage or permit.
Third, and most European countries fall into this category, some governments know perfectly well that the Internet cannot be governed, and that insofar as it can, the US is not going to hand Icann over to the UN anyway. This means they can posture all they like, and suck up to China and Saudi Arabia, knowing that it is going to make no difference at all.