I support the IANA transition but the proponents also stretch the truth. Nothing important will change no matter how this resolves, because ICANN has little real power. ICANN, a once obscure agency, maintains the Directory Name Service, DNS. If Vladimir Putin or Donald Trump takes over ICANN, they couldn't effectively use it to censor. The Internet is a network of networks. The "infrastructure of the Internet" is actually controlled by AT&T, France Telecom/Orange, MTN South Africa, Russia's Sistema and the other carriers and backhaul systems. The DNS is just one possible way for those networks to communicate. If ICANN becomes a problem, those companies can and would move to another system.
Andrew Sullivan, Chairman of the Internet Architecture Board, notes, "Other name systems have been invented and deployed, and they don't depend on a root zone. Also, even if we keep using DNS, nobody can force you to use the same root zone. ... If the IANA system ceases to be useful (or starts to be too politically controversial), then people will choose something else. And there is no central point where people could be forced to use the IANA system because there is no center in a network of networks. That is also the reason why nobody -- not China, not Russia and not the bogeyman in the basement -- can 'take over' the internet."
Ted Cruz is a bleeping idiot thinking ICANN could be dominated by the Russians or Chinese. ICANN's Chair is Steve Crocker, who has worked alongside Vint and others to build the Internet since earliest days. Also on the board are George Sadowsky, who had a distinguished career with the U.S. government; Marcus Kummer, who served the Swiss government and then was ISOC's policy lead; Thomas Schneider, currently of the Swiss government; Ron de Silva, of Time Warner Cable in the U.S.; Jonne Soininen of Nokia; and a half dozen others with generally concurring views.