If the US had a normal President, this might be rational enough. As things stand, we're a whisker away from a war which will incinerate millions, kill the world economy stone dead for decades, and prevent all progress on the many critical issues facing our dying planet.
The president is a non-issue on strategic matters, he has no knowledge on this, he knows it and the people around him know it. If you watch him, you'll see him do the typical alpha-male thing solely for his crowd, then the generals will tap him on the shoulder, whisper something in his ear, and after that he will do and say what he's told. Happened for Syria, happened for Iraq, happened for Afghanistan, and it will be the same for NK.
True
> he knows it
I've seen no evidence of this yet
> it will be the same for NK
We'd better hope so, but the clear first rule of thinking about the future is to give scant attention to anyone who expresses much confidence in their own prognostications. No-one knows what will happen, because the future is undetermined (read Tetlock amongst others: political predictions are difficult and generally of low accuracy).
Don't forget that the whole design of the US nuclear deterrent system is precisely to make their use not "strategic", but keep it rather within the tactical ambit of the POTUS (for an expert description see https://www.washingtonpost.com/posteverything/wp/2016/12/01/...). So if in a fit of pique Trump decided to 'teach Kim a lesson' (this is the level of sophistication at which he thinks), "the generals" may well tap him on the shoulder, but it will be entirely a matter of his whim whether or not he heeds that tap.
Your retreat into comforting certainty is quite understandable.
Nrk is spending massive amounts on military but probably is losing to South Korea. Nuclear weapons offers nrk a way out of being outspent.
The west accepted Pakistan as a nuclear power; my guess is that we will accept nrk as well.
Single out the US isn't helpful for the discussion. Do you think Russia, China, EU have all just stayed away from all of the conflicts? How about Iran, Israel, Saudi Arabia, even Turkey?
Ask South East Asia countries what they think of China; or ex-USSR states of Russia; or Sri Lanka of India.
North Korea has the support of China and holds South Korea ransom. They don't need nuclear weapon for self defense.
At a guess, once you are a nuclear power, absolutely nothing.
To be clear: I think the Government of NK is monstrously evil, and I wouldn't shed a tear if their population rose up and lynched them.
But their behaviour in seeking nuclear weapons is rational, because history has shown that non-nuclear dictatorships with valuable resources get invaded.