Strategically for the U.S. a nuclear armed S. Korea and Japan would help U.S.

But, here's the thing. If I was an average person in one of these countries I might not want nuclear weapons there. Because if your country has nuclear weapons you are actually more likely to get hit by nuclear weapons from another country if a real full on war ever breaks out than if you don't have nuclear weapons.

This has been the biggest problem of living in the U.S. since World War II. Both Russia and China targeted us with their nuclear weapons. (And this is likely still true today). So, if there is an accident who gets nuked? We do and so do Russia and China. Basically if there were an accident every military installation and big city in the U.S. likely would be gone along with all big cities and military installations in Russia and China too.

But, the rest of the world might be okay (until they all started fighting with each other over the vacuum of power) with Russia, China, and the U.S. all gone. So, Russia, China and the U.S. would all be 3rd world nations for 20 to 50 to 100 years and could be taken over by other nations who might be angry who were not nuked.

To me, strategically, this is the main reason why nuclear wars (or any wars) don't happen with Russia, China or the U.S.

So, if you don't have nuclear weapons as a country you are more likely to be taken over by a country who does.

But, if you do have nuclear weapons you are more likely to be destroyed by them too.

However, all this being said, "It really would be to the U.S. advantage strategically to have both Japan and S. Korea nuclear armed. So, I'm thinking doing this secretly (so only China's military knows about this actually might happen as a result."

In other words the U.S. should or would do this.

In fact, it is quite likely we already have because of the weapons grade plutonium being reprocessed at Fukushima that melted down in one of the meltdowns.