One IP or AS number is just like another, so all you need is a simple administrative body to make sure two people don't try to use the same one.
Yeah, true with current or foreseeable future protocols. Not necessarily impossible to avoid, though - what if networks were addressed by public keys in a large sparse space, and you could just randomly generate them when needed?
That's a source of endless disputes, and so long as those domains remain a source of substantial income that will be the case. So a body is needed to resolve them.
You're presuming I recognize the legitimacy of intellectual property there, I think. I do not, and see no reason to object to "whoever claims it first owns it".
On the other hand, DNS is probably the most administratively problematic protocol around due to the need for someone to run the root zone. That one would sure be nice to find a workaround for....