You ignore the fact that he doesn't think like a rational person - kind of like Neville Chamberlain did with Hitler. 

What if NK thinks the U.S. will not retaliate with nukes because the U.S. government doesn't have the political will to use nukes? I could see such a situation arising if we had another president like 0bama. 

You're also simplifying the situation and not considering other possibilities. 
If the NK regime is allowed to develop nukes, what makes you so sure it won't proliferate the technology to Iran and other rogue states?

What makes you think Japan and S. Korea won't decide to nuke up if NK is allowed to continue it's development of nukes?