You don't need nuclear deterrent to deter someone that can only launch one strike at best. We can maintain a deterrent by making it clear that if you ever use a weapon, your entire government will be removed, you will be out of power, your kids will be out of power and no one within 6 degrees of separation of you will ever hold power again.
We can do all that without resorting to a nuclear strike or carpet bombing of cities.
The North Koreans are already cut off to a large extent and have maintained power through a martial state. So removing their leaders from power will require dismantling their military. That is probably the most unappealing and downright shitty assignments I could possibly think of. North Korea might be insane, it might be starving but it has been locked in a siege mentality for 60 years. I am sure the mountains along their borders are some of the most heavily fortified and bunkerred positions on the planet right now. Nothing fancy, just thousands of miles of tunnels and concrete (minus the reinforcing steel).
Going in and taking North Korea in a ground war is going to make Iraq and Afghanistan look like a fight at recess. The North Koreans are weak in terms of supplies, but not bodies or resolve. They will be able to bring more men to the fight than we can right now. Sending in US troops to North Korea would be the all time dumbest mother fucking move anyone could ever make ever right now.
The regime needs to fall first. Then we can think about moving in.
But how so? We need to bash in their skulls before that would happen right? Nope, They want a fight. They have wanted a fight for six decades. If they get a ground war, the complete rivers of bull shit propaganda thy have been spewing forh will suddenly be legitimized. Every good NKer will rush off to save their country and no one will want to miss possibly the only opportunity to become a real war hero. The kind that have been idolized since before most of them were born. Fighting North Korea will solidify the regime's hold on that country until the last man, woman and child has given up their lives for honor.
So no, threatening them with war is not the deterrent you might think it is. Nuking them, even if they nuke us, will still get them a lot of sympathy and something to show in their recruitment videos for the next 100 years. We would have to utterly destroy every spec of their military command, and even then it would turn into another asymmetrical war after that.
If anyone was serious about dismantling North Korea 1.) It would have happened already and 2.) It wouldn't require a single bullet being fired. In a country that is so desperate for resources, corruption is king. Bribes on top of bribes on top of favors is the ONLY way anything happens there. The political infighting and shuffling is tremendous among the rabble. So this is where you take advantage of the situation. You start buying people, on a massive scale. You undermine the machine by compromising everyone. And then just start exposing them by giving information to their rivals. This is not easy and requires that you use North Koreans for everything. But the purpose is to just cause panic and pandemonium within their ranks.
If every major and minor official has been bribed in some way, you can let the North Koreans dismantle themselves as one controversy after another hits. If you infiltrate their news agencies you could even air some dirty laundry in front of the public. Doubt it would do much good as they have been a self censoring society for ages, but it would complicate things for them as people wouldn't know what the party line was anymore. The military structure needs to be gutted, soldiers need to be sent home or wrongfully accused and discharged or executed. It would take a while, and probably wouldn't completely topple them, but it would be 1000 times more preferable to a frontal assault; and make sure they had far from a unified front if we did.
End of the day I would set up some puppets that kept calling for reconciliation with the south. That is the only way this insanity will end, is if the country is unified.
But that is not what anyone wants. Either they want a new conflict to sink their teeth into, or they don't want reconciliation. Whatever the motive is, everyone involved has been taking all of the proper steps to escalate the situation. I think with Iraq and Afghanistan essentially out of long picture for conflicts, we need a new playground. So if we get nuked, that's all the justification in the world to spend another 20 trillion fighting terrorism for the next 15 years.