The North Korean government collapsing is the best case scenario for the US. They don't have to worry about the fallout from a military conflict. That's why they want China to cut-off the North because a self-imploding collapse is more likely. Whether China cuts-off North Korea or the US exploiting North Korean paranoia to have them cut-off relations by saying China is working with the US, lie or not, works to that end.
A collapsed NK government can very easily give China an opportunity to set up a government more amicable to China, as it's in the best position to do so, and it would not necessarily alter the nuclear trajectory of NK. There really isn't a great scenario for the U.S., which is why successive American governments have done nothing different for many years.
There IS a best case scenario for China though, which is for the U.S. to start the war, get blamed for all the carnage and destruction that would surely ensue, and for China to finish the war and use the gains of the war as well as its ability to rebuild the peninsula to draw SK into its orbit and expel the Americans from the peninsula. It's a risky and costly move, of course. The safest good scenario for China would be for NK to denuclearize and resign itself to be under China's protection, basically becoming a more China-friendly version of its current self.
