Yet this threat is unprecedented. Ending a 70-year-old truce, promising(!) a preemptive nuclear strike! These threats cannot be ignored or pacified in the same way as a gunboat firing at a fishing boat.

To be honest, dismantling their military regime, opening their borders and requesting help would be more effective.

Not if the aim is retaining permanent power for Kim Jong-un and the military junta that actually runs North Korea.

There is probably a Pareto improvement that could be made by agreeing to hand Kim and the other leaders almost any amount of material wealth in exchange for them stepping down and allowing South Korea to govern North Korea. It would have to be better to live in a first world nation with hundreds of millions / billions of dollars than to be the Great Leader of North Korea. I guess the fact that this doesn't happen just goes to show how much better sovereign power is than money.

Absolutely, if you could figure out a way to make that deal without Kim executing the 'traitors' first. Those plots, like valkyrie, are always exceptionally risky. There's no doubt plenty of the Hitler style demigod fear is present (not necessarily with the top of the junta, they know Kim is just a puppet, but everybody else).

Would South Korea want to govern North Korea?

For everyone except the people in power.