This implies there is someone who could take over that can be trusted. I'm not convinced there is, personally. The question then becomes "Who do you trust more than the US" in this context. I think the answer to that question would be more interesting.
At the end of the day, someone(s) will be in a position to "pull the plug" or just alter the machine in some way. I think your view is a bit naive. The machines have to be physically located somewhere and they're going to be open to vulnerabilities because someone needs to perform routine maintenance. There will also need to be a group or organization to oversee the day-to-day operations and handle things a machine can't. It's yet another avenue for corruption. Your ideal "control" simply doesn't exist and cannot exist. Someone has to be in control.
It reminds me a bit of the whole superpower conundrum. There are those who want the U.S to step down as the world's police. The question then becomes, who would replace them? This question confuses those people because they do not grasp the whole "nature abhors a vacuum" aspect of the problem. They also ignore the human element, which is that people are greedy, corrupt and power driven. Especially leaders of countries. These people want the U.S gone but won't connect the dots further to see what would happen, and what life would be like without them acting as the world's sole superpower. What would happen is another entity would step in and fill the role. That is guaranteed. It's a certainty because nations have been fighting wars for that mantle since before WW1. And I'm sorry, but I prefer the U.S to China or Russia. They're simply the lesser of the evils. And not by a small amount.
To deny it is to deny the fact that Russia and China would stand aside and not make an attempt to grab that power. Do you honestly believe China or Russia won't leap at the chance? Let's say you honestly do. Ok, so then the question becomes, "What about 25 years from now after Putin has died and there's a completely new administration at the helm. Can you say that they won't grab for power?" It doesn't require people not leaping to grab that power today, but for all time in the future. And believing that someone won't eventually grab for it is beyond naive because it's denying human nature.
There is a perception of Switzerland's stance on privacy becoming increasingly weak as time goes by, showing that their convictions at the very least are becoming diluted in favour of international pressure.
The guy who used to manage the Australian .au TLD.
The problem I see is that since ICANN is located within the US, the system will still be abused, because ICANN falls under US jurisdiction with all its moronic justice system and draconian, though generally ineffective, "intellectual property" law enforcement.
So nothing will change anyway.
Now, with that being said I'm very much supportive of "pirating" in that I don't believe that it's stealing since that would mean corporations are entitled to potential future profits.
Another thing you pointed out was how ineffective it is. And you're right. Basically nobody cares anymore unless you're making a noticeable amount of money from doing so or just generally doing something other than pirating stuff.
Aside from questions about intellectual property, I think the U.S. generally has pretty great laws regarding the Internet. Compare that to, say, Australia where vaginas that don't look "normal" are banned, or the outright censorship in most of the world. With the U.S. being the epicenter of the software industry for the time being, it's very sensitive to any regulation or law involving the Internet.
Unfortunately, the US has used the domain name system to fight piracy without due process in other countries rather than acting within their own jurisdiction and closing illegal servers within their own jurisdiction. That's an (a) abuse of the domain name system, which is (b) technically inefficient -- just use an alternative root server --, and (c) hitting the wrong people such as people who merely put links on their web server rather than those who actually infringe copyright.
Because of this documented and patently stupid abuse of the DNS system the US ought not control the root servers, not because of US laws or anything else related to piracy. I couldn't give a shit about piracy, but I do give a shit when some server that is perfectly legal in Spain suddenly becomes inaccessible and replaced by an FBI logo, just because some technically inept dumbass judge in East Texas thinks so.
Whether other countries would do better than the US is debatable. I'm glad you like the laws of the US so much, but have a hard time sharing your opinion about them and can think of various more worthy candidate countries for the label "best laws".
My guess is not. gTLDs run by registrars not operating in the U.S. nonetheless probably sign ToS agreements with ICANN that effectively permit seizures by U.S. authorities. But for ccTLDs I doubt this is the case (it's hinted at in this white paper, https://www.icann.org/en/system/files/files/guidance-domain-...).
If you want to run a Pirate Bay or something, you're probably safest registering a domain under a ccTLD for a country with a lax policy.