North Korea built a nuclear weapon because they're acting rationally. Nuclear weapons provide them legitimacy and bargaining power, both domestically and internationally. It's the same reason Iran wants a nuclear deterrent, or anybody else for the matter, like the U.S., China, or Russia. When you have the bomb, other powers tend to tiptoe around you--see, e.g., how Pakistan sabotaged US interests in Afghanistan with no discernible repercussions.
The real threat from North Korean nuclear weapons (other than empowering North Korea geopolitically) is in proliferation. And that's probably one (albeit minor) reason everybody tends to look away when they skirt the embargo.
From a proliferation perspective, Pakistan would seem to be a greater threat than North Korea. There is strong evidence that Pakistan actually sold nuclear technology to North Korea (although it's unclear whether NK used that technology in their weapons program).
That's assuming they'll be able to scale it. Having a few low-yield nukes doesn't buy you much in terms of offensive capacity, especially not against "old" nuclear powers. But what it does is give you sovereignty - which is why I think NK wants to have those nukes.
The reality of modern world is that nuclear powers get to push around every other nation without consequences, whether overtly (like US getting away with invading two countries in the recent years) or covertly (proxy wars). But the world sees the use of nuclear weapons as qualitatively different from conventional ones, so having even one nuke you can threaten other countries with seems like an effective way to deter other powers from bullying you too hard.
I wonder about nukes being of value during "day-to-day" diplomacy. Does even NK really go into negotiations with China for access to oil or something with the argument "sell it to us or we nuke you!".
I only see it as a deterrent for invasion. The US and South Korea will think twice before drone striking Kim if they know there could be a nuke in the air.
For any other diplomatic purpose the other party must surely just walk away when the "or we'll nuke you" argument comes out?
Yeah, I don't think nukes matter "day-to-day". But there's a constant awareness of them in the background, much like there is a constant awareness of general military situation.
On the negotiation table, there's only so far one nation can push another before the other one starts considering military options. There's no sharp line here - economics and war are parts of the same spectrum. Usually, it's in the best interest of every party to stay on the "economics" side of the talks. Both parties having nukes makes both of them try harder.
NK could at most destroy a few square blocks of e.g. Seattle. That would be a tragedy, but it would also serve as justification for a multinational coalition (possibly even including China) to take over NK and ultimately hand its territory to SK.
IOW, if NK lobbed a nuke anywhere they would cease to exist. I'm pretty sure Mr. Kim understands that.
The real threat from North Korean nuclear weapons (other than empowering North Korea geopolitically) is in proliferation. And that's probably one (albeit minor) reason everybody tends to look away when they skirt the embargo.