Earlier quoted context omitted.
Only one intelligence left standing is an outcome that most people would find negative. It's like if Skynet was the last survivor of the Terminator franchise. Why would anyone want that outcome?
I think the Borg, if successful in assimilating every known intelligence universally, would be a more appropriate analogy. As to why they would want it, I can only speak for myself but I think it's the most logical outcome if you extend the concept of self awareness to the universe.
It's the same as arguing that the replicators on Stargate SG1 should be the logical outcome. Technologically, they are superior, but they're not a preferred outcome. Similarly, one could argue that gray goo or Carpenter's creature from The Thing are superior, but we don't want a world of gray goo or things.