I think in terms of total probability, the US is more likely to launch a nuclear strike on DPRK than it is to invade and fight a ground war there.
DPRK is armed to the teeth with conventional weapons and has had 60 years to dig in deep, making a conventional ground assault extremely painful. Not that the US couldn't *win* such a fight should it choose to dedicate the resources, but it would be extremely resource and manpower intensive.
And for what possible gain? No appreciable natural resources, a civilian refugee crisis of epic proportions, a diplomatic shitshow with China and Russia, both of which would use a US commitment to pursue every bit of mischief they are capable of and a price tag in the trillions. Not to mention the global economic ding from the likely destruction Seoul and the disruption to a not-insignificant part of the global supply chain.
Kim's nuclear ambitions are equally ridiculous. They're decades away from any kind of reliable and effective long-range nuclear weapons program and even when they get to the point where they have a half-assed accurate ICBM that can deliver a half-assed effective nuclear weapon, what are they going to do? Any serious *attempt* at using it or even believably threatening to use it, faces the existential threat of a US retaliation that would annihilate them, something that not even the USSR at its peak could avoid, either.
Which is all a great and pretty accurate assessment of why all of us should selfishly leave the North Korean state alone. The humanitarian plight of North Korean
civilians is just so much collateral damage that we will accept, and more importantly not talk about. The multi-generational dictatorship run as a slave state will continue to leave about 25 million people living under a crime family that runs things like an Egyptian Pharaoh. Complete with worshipping the past, present and future rulers as deities. the only meaningful difference is that instead of a national effort to build pyramids, they are being driven to build nuclear weapons and rockets to deliver them globally. Ignoring the humanitarian catastrophe for the last decades has just made it worse, the future will too.