The American run ICANN functions as pretty much as a post office: they assign addresses, delivery protocols, and, deal with mostly technical matters of keeping information flow efficient. No political interference comes from ICANN.
The countries mainly opposed to the United States maintaining an American invention are Brazil, China, Cuba, Iran and several African Muslim nations. All of which are oppressive of their people, advocate stringent political censorship of their citizen's internet use, and vigorously violate intellectual property rights.
The internet is successful because it is run by people who American capitalists who believe in openness and free market efficiency, and not socialist demagogues. Keeping ICANN in place essential.