First thought: If China is okay with it we have nearly nothing to lose and would likely have the public's faith restored in our military. Everyone saying it will be like the middle east aren't taking into account the circumstances and difficulties of such a cluster fucked area. North Korea doesn't not have hundreds of tribes with half a dozen ethnic groups that hate each other. They also are very poor and ill educated, I personally doubt they can afford an AK in decent condition (Let alone the government actually being desperate enough to give one in advance, the last thing a dictator ship does is arm its people), or have the know how and capability to maintain a resistance for long. In Afghanistan, they had received previous funding and training from American CIA operatives to help counter the Russian invasion From there it was s snowball effect of experience leading to training, which still resulted in an absurd causalities dissonance between Coalition and n Afghan forces. Along with a failure to kill or capture the majority of Taliban infantry.
Especially if the US has prior agreements from China to not help North Korea at all, meaning no training for IED making, no equipment to make bombs from, and the only thing they really have in war materials are illegal chemical weapons, which will likely be more likely to kill the user, since they won't have access to chemical protection gear while Coalition troops will. This may be idealistic of me but as soon as they start getting fed (Which a lot of people are not or are just scrapping the bottom of the barrel), and see that South Korea is actually really good, which despite what the Kim's propaganda proclaim constantly, everyone but the most fanatical knows that he South is better, only the most fanatical will stay to fight while the rest return home or go see family that is on the other side of the border.
And before people say they will use their massive artillery stockpile, or nuclear weapons, it should be noted that while the artillery is a problem (If the military even bothered springing the enormous amounts of cash cycling out their ammo constantly to avoid misfires, duds, ect. Which i doubt from the very poor nation.) the Nuclear weapons (Launched by missile or aircraft) Will be nullified by American air superiority and intelligence. We won't just declare war before we're ready, in all likelihood it will either be NK attacking first, or an agreement with China to allow us to launch a surprise attack which will allow us to gain air superiority before the NK planes can even launch. From then on any artillery piece that opens fire will get bombed.
The biggest loss will likely be Seoul, even if you get a majority of people into underground shelters, and even if a majority of enemy shells are just duds, the damage will still be catastrophic or problematic, they can rebuild alongside North Korea and may even serve as a catalyst for SK involvement in peace keeping duties if spun right. Either way, the US administration will and should wash their hands of the area as soon as possible and give it to South Koreans to maintain. They are rich, of the same nationality,ethnicity, and language which already solves most problems of a foreign occupation with the drive to help their brothers across the DMZ.
Second Thought: American Shock troops and aircraft superiority, with South Korean and Japanese ground forces fording the way, the war will be drastically shorter then the planning period (Months to a year of combined planning, compared to a few days or a few weeks at most for the surprise.) All of the above still apply, but Seoul will probably be saved by SK counter artillery, and the desire of NK leadership, if they have any competence, to rather arty the troop formations coming for their heads.
Third Thought: War won't even start, Kim Jung Un's head will be on a pike before the first shot is fired with a total surrender. What ever the regime did to make CHINA angry, will likely have the military literally screaming for their heads. No way they can even begin to fight a 360 degree war, likely with the Chinese uncaring about Civilian causalities if THEY of all people had to get dragged in.
Best part is, since we have no economic, or political interests in North Korea, we can just kill their political and military leadership, and then just leave, no need to even kill their soldiers or even occupy the land. Who in the US congress honestly gives a fuck if that shit hole collapses upon itself in civil war? The South Koreans will see this as an opportunity to reunite the nation. And even if they didn't China's only interest is to keep it American base free.