Sounds more like sabre rattling more than a real threat. It's not like SK or Japan couldn't complete their own nuclear weapons programs relatively fast if they really wanted to, and giving them those capabilities changes nothing for the US. On the other hand, should China chose to retaliate, it could pick any one of a long list of countries the US has managed to piss off. Countries which are too poor or not technologically advanced enough to have their own program. Proliferating nukes throughout the Middle East, Africa, even South America, would divert the US attention, and end in a "death by a thousand cuts". Going through with this idea would be all risk and literally no gain for them.I am not sure the u.s realize they don't have any leverage to force China on arms control. They already have nuke submarines capable of striking China from first island chain. Nukes in Japan and SK won't make any difference
They could have put nukes in SK the day NK tested nukes decades ago but they didn't. That tells you a lot