...but the U.S. and the Soviet Union were never really threated with a third-party nuclear conflict prior to the end of the Cold War. One could make an argument that India and Pakistan would fit that description, but neither nation's allegiences were that strongly held with either country during that period.
The same could not be said if North and South Korea ever engaged in a nuclear battle on the Asian mainland in the here-and-now. China would be forced to secure its safety and sovereignty at all costs. I sincerely doubt they would leave such decisions in the hands South Korea and/or the U.S.
Or Japan for that matter. They will understandably freak if Korea becomes a nukefest. In my opinion, they would kiss nearly 70 years of military defense practices out the window in a microsecond if that happen. The whole Far East Asian theater would be completely unmanageable when that happens.