US wants SK to have to rely on the US for economic and military needs. Of course the US doesn't want SK to have nukes. It's good for SK to have them though.
Little known is that the core of Korean culture is based on a clan system, and that there is a powerfull connection between north and south, making the impossed division much more tenious than what appears on the surface. Reunification is the thing that all of the outside powers are working to prevent, but are now facing a situation where demographics, alone, will dictate how things will procede.
A unified nonaligned sovereign nuclear Korea would be a disaster for continuous US plan to divide Eurasian continent. A chance for the rest of the world.
I don't think people in the US realize what really happened in the past 2 months.
Pax Americana is dead. Full stop.
There are a lot of countries able to develop nuclear weapons, and after decades of voluntarily restraining themselves, now they will. Every single one of them. USA is no longer trusted as an ally. There is simply no other option.