While I don't deny long range missile strikes would likely be part of our strategy, they would be unable to achieve our objectives. The NK military more strongly resembles a WW2 military than a modern one, its not concentrated in a few high-tech assets that can be destroyed, the soldiers are fanatical and fully willing to live off their own land if it comes to that. Nuclear missile strikes could be preemptively stopped for sure. But the artillery aimed at Seoul is numerous, spread out, and already zeroed in on the target. Destroying fire control facilities does nothing about that, wiping out individual artillery pieces and ammo storage helps but there's a lot and they don't need to fire that many times to be effective. Nor do I think the NK infantry be easily crippled or frightened off. Although I do think that we could sweep them aside in land warfare, with merely heavy losses (probably mostly from artillery), that's never been the question. Nor has NK's ability to hit us with a nuke historically been the problem. Our objectives would be to achieve a rapid and bloodless (or rather, not "historical humanitarian crisis spanning the whole region") victory, and missile/precision strikes change about nothing about that.
I don't think the North Koreans could Vietnam/Iraq us and force us to leave. But, well, they don't need to to make the situation horrifying. Simple infighting, or WW2 Japan style "you're fighting to the last man, woman and child and you're going to enjoy it!" tactics, or resistance propaganda/reprisals interfering with us re-educating the population. It all could make the whole mess a nightmare without killing a single American. On top of that, NK is very "top heavy". The military and political segments are bloated, consuming a disrpoportionate amount of education, employees, and supplies relative to the civilian population. So the issue becomes, obviously ruling party members and soldiers/officers are an obstacle to victory. But if you kill or imprison all those people, there's nothing left. There's no education, little to no physical property, little leadership and few healthy people among the remaining population. And that's a problem we had in Iraq; by our harsh suppression of the ruling party we alienated the only people left with any real control of the population. How do you NOT do that in NK?
As for China intervening in a conventional fashion... Like I said, land war between nuclear powers gets weird. Like what's kosher? Uranium rounds, tactical nukes, conventional weapons with yields similar to tactical nukes? Are ships and planes on the table? Can we use vehicles with nuclear reactors? And what does victory even mean when both sides have an answer to the other side "winning too hard?" It just requires a lot of... cooperation, to have a largescale land war between nuclear powers. You have to work out a lot of very specific ground rules and a shitton of trust since you're going to be at maximum nuclear alert the whole time, and firing long range missiles that sure as hell could LOOK like nukes to some overworked radar crew. And it would have to be a land war, because China has nothing on us when it comes to the "fling missiles over the horizon" game and they know it. This shit is why we have proxy wars, its a lot easier to just both hum a nice tune and pretend you aren't fighting each other at all.