Of course, people with strong opinions fall into two camps: those who wish to maintain the status quo and those who wish to see control over the root DNS servers relinquished to a UN organisation.
There are two arguments used by the proponents of the status quo: "If it works, don't fix it" and the freedom of speech argument.
It is true that so far, the internet has been working well. The tremendous growth of the internet in recent years has not provided lots of problems -- technically, there are no objections to the way the ICANN manages the servers.
However, as the internet gains more and more weight, as more and more business and government transactions are conducted over the internet, the internet becomes a vital part in the economic life of a country. The question is: do you want control over that crucial instrument in the hands of a foreign corporation that is under the control of a foreign governmental body? I can imagine that, out of principle, you do not want crucial infrastructure in the hands of a foreign government. The internet is much bigger than the US alone, and it would be good to establish a more neutral form of control.
The Galileo Positioning System is a good example of this: the EU finds that positioning systems are crucial to commercial and governmental interests, and thus can't tolerate that these resources are managed by a foreign government. Yes, it's expensive, but Washington won't be able to shut it down at will.
The proponents of the status quo object that a 'rule by committee', as a UN-instated internet governing body would undoubtedly be, would be too slow to adequately deal with the issues that will surface. I'm inclined to agree with them, but it is not entirely clear to me what issues demand immediate action (other than technical issues like server outages, but that's not the problem). Granted, generally speaking a corporation is much more efficient than a committee, but you must realise that the ICANN has a monopoly -- and the rules of the free market don't apply to a monopoly. In fact, it is precisely the inertia of the committee that could save us from a capricious corporation that wants to achieve goals that are not necessarily in everyone's best interest.
Then there is the free speech argument. It is telling that amongst the countries seeking to wrest control of the internet from the US are Iran and China -- countries whose governments aren't, shall we say, known for their love of freedom of expression. The internet provides means for dissidents to communicate with each other and the outside world -- vital for democracy. It is feared that the new governing body would be dominated by these undemocratic regimes, allowing them to impose their censorship over all of the internet.
This is indeed an important issue, one that is not to be taken lightly. However, in recent years the US has shown itself to be less and less concerned with civil rights. Who is to say that the US will not block future developments, like they did with the .xxx top level domain? National concerns dictate what the rest of the world can and can not do on the internet.
It might very well be the committee-inertia that saves us from these national considerations, if it comes to that.
In conclusion, I am not satisfied that the ICANN is the only and best way to govern the top level DNS servers. I would like to see more international control and a less US-centric view, but I am suspicious of the motives of the likes of China.