>South Korea and Japan should acquire nuclear weapons
Ideally yes. Would love that. But almost never-never-never gonna happen.
Culturally, Japan does a much better job than most in teaching (and learning from) war history. Hiroshimaa and Nagasaki are still quite fresh in their minds. They're not Germany; Japan still identifies as, acknowledges being, and is deeply ashamed that they are the same nation/people that bombed Pearl Harbor and fought in WW2.
The power plant meltdowns also don't help, but is probably less culturally entrenched.
Only chance of changing that is maybe one-day for parity with N Korean capabilities, or an imminent major war with China.
It'd be... historically & culturally interesting, if Japan accepted US nukes or technology as assistance in a wartime emergency. Could potentially create one hell of a bond between allies, if played right. Or a whole lot of hate, if Japan's public opinion isn't won over first.
As for South Korea, and in the context of North Korea:
As long as N Korea is N Korea, I don't know if we want to just drop nukes into the equation, as is, unless we're talking about US-controlled weapons-sharing. With the downside of being a less effective threat due to direct US involvement, and culpability.
What would be ideal is:
Somehow make Korean reunification happen, under a democratic government that inherits NK's nuke program. And then advances it with US blessings and/or assistance (either openly or modeled on something like the Israeli program).
Japan won't like it, but it also might be enough to encourge them to overcome their aversion, Hiroshima/Nagasaki be damned.
It would require overcoming a constitutional ban, so not easy. But they make an increasing number of exceptions for weapons constitutionally limited to "defensive capabilities," which somehow now includes two aircraft carriers with F-35Bs.
And which China already hates.