Yes, US control of this piece of the internet is a fossil of the 20th century that causes more trouble than it fixes.
No, there are too many bad actors out there that would take advantage and there is no compelling reason to give up anything.
Maybe, but only if we maintain enough influence to veto anything stupid or malicious to a free and open internet.
Who cares? Politicians can posture all they want, it's still just domain name registration and not the internet.