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You said yourself that it would be at the expense of hundreds of thousands casualties...It's probably a worst-case estimate. It really depends on the efficacy of allied counter-battery fire and air capabilities versus enemy artillery positions.
There's also room for creativity. Park a carrier battle group off the coast of Seoul and fake a serious reactor event during a period of easterly winds, with mandatory evacuation southward in the days prior to the invasion.
>...not even counting the consequences of possible nuclear war.
If you're referring to North Korea: I'm not advocating invasion presently, merely lamenting that NK was not confronted prior to acquiring nuclear weapons. Invasion today only works with absolute assurance you can neutralize NK's nuclear capability, and that's extremely difficult if not impossible.
If you're referring to China and Russia: I'm pretty sure that to them, North Korea is squarely not worth risking nuclear confrontation with the United States over.
>That's a pretty bad argument for a moral justification for an invasion, don't you think?
No, I don't. There is an almost equal number of people languishing in hellish prison camps—some their entire lives—with a far greater amount in the general population living meager, miserable existences.
The very nature of it should transcend simple body count calculations in all but the most extreme cases of disparity. The civilized world has a moral obligation to wield its power in such a manner that doesn't allow such suffering to exist, even if doing so incurs a heavy cost.
Can you imagine if World War II had a different outcome, with Nazi Germany contained yet retaining its statehood? The term "Holocaust survivor" probably wouldn't be present in the modern lexicon. Such fiction isn't too dissimilar from the plight of North Korea's political prisoners today. By and large the civilized world doesn't give much of a shit about them.
When airmen go down behind enemy lines, the forces available to rescue them don't say "Well, we ran the numbers and it's not worth the potential cost of a rescue mission. So, we're just going to forget they exist instead." Esprit de corps ensures a moral obligation to do the right thing regardless of the risk.
I'm simply advocating for the same ideal on a basic humanitarian level.