Yes, I know they are a bunch of libs but they didn't build great companies without some brains and a lot of lawyers. If this giveaway was dangerous to their health we would hear about it.
But we don't. It's so quiet you can hear ...
That's because it isn't the apocalypse that some people want to believe.
All the US did was cede oversight of the organization that controls the root DNS servers.
What are the root DNS servers? They are effectively the global address book, mapping domain names to IP addresses.
You don't normally request information from the root DNS servers. You ask your local DNS server (normally operated by your ISP) for the IP address of freerepublic.com. If your local DNS server doesn't already know it, it asks the root DNS server, then sends it to you. Your local DNS server then keeps the address of freerepublic.com in its cache until it expires automatically.
So, let's pretend that ICANN is unduly influenced by someone in the future to remove "objectionable" websites from the root DNS server. All that means is that it is no longer in the global address list. The website doesn't disappear -- you just need to know is the IP address.
But, how do you know that IP address? The answer: use an alternate DNS server. If ICANN starts censoring the root DNS servers, you can expect alternate DNS services will pop up and provide the "missing" domain names, in addition to everything in the root DNS servers. It's very easy to modify your computer, phone, or home router to use the alternate DNS servers.
Who will operate these alternative DNS servers? There are two already in operation: Google DNS and OpenDNS. You can use them now, and their service is usually superior to the DNS servers operated by your ISP.
I've found that complaints of "my Internet isn't working" is usually caused by a slow DNS at your ISP. The classic symptom: you enter a new website address, and it says: "server not found". You wait a few seconds and try again, and it works. If you are seeing that on a regular basis, try changing your DNS server. Both Google DNS and OpenDNS provide tutorials to do so.
I'm not claiming ceding oversight of ICANN was a good idea. But, it isn't the crisis that many want you to believe. The Internet is far more resilient: it treats censorship as damage, and is easily circumvented.