It is not like North Korea is putting all its chips with China nowadays. If it was, it would not have gone out of it's way to go nuclear. Nor would Kim have purged all his top officials with links to China.
And how would conquering South Korea help China in it's war ? It does not deprive the US of its ability to operate in the region, it still have bases in Yokosuka, Guam and Okinawa. It does not defeat a major contingent of US assets in the region. South Korea only has 20,000 thousand US soldiers and 0 aircraft carriers or strategic assets.
If China is doomed to lose a naval-air war with the US from the start, invading South Korea will hardly tip the war back to its favour. Worst comes to worse, South Korea can fall and the US can still fight on just as well.
And that fall will not come easy for China, I don't know that it is about people talking about a Korean war rerun, but let us just rerun the figures for once. If China wants to invade South Korea it will have to not only potentially fight North Korea which while weak can still put up a fight or at least be a passive aggressive partner that constantly hampers Chinese operations, it will have to face off against a half million strong army, backed up by one of the largest airforce and navy in the region. The only way China can ensure that it will have a distinct advantage would be if it concentrate a good portion of it's naval-air and land assets in the region, assets that are needed to face off the US. In fact, invading South Korea would result in a spectacular backlash for China at worse, and a meager morale boost at best. Capturing the US 2nd infantry may sound good on the media, but it does not address the issue of US carriers plying the East China Sea, or bombers taking off from Guam or Okinawa.
No, North Korea will wholeheartedly support China, if China decides to fight South Korea.
That is an absolute given, and your scenario where North Korea resists is simply wishful thinking.
Not enough people understand that this is the ruthless logic of regime survival for both China and North Korea. And too many American admirals are ignorant about what would happen.
And so what if South Korea can field a hi-tech army of half a million soldiers? South Korea is a SMALL isolated peninsula whose industrial capacity will be devastated in any war because the entire country is within range of China forces.
I also understand that the dark joke at some of the US-China conferences is that China has an excess male population of 40million. And China does have enough strategic depth and industrial capacity to field an absolutely huge hi-tech army. And that army will bleed US reinforcements and potentially conquer South Korea, given some time.
In that time, we can expect the US to pour in more soldiers/aircraft/ships into the Korean peninsula to prevent the conquest of South Korea by China.
Those aircraft and ships will not be available for operations elsewhere against China, and would have to operate right in the teeth of Chinese A2AD forces on the North Korean coastline. So we would see a rerun of the last Korean War, except that this time, China would have the capacity to win.
So what would be the political impact if say 20,000 US soldiers are marched into prisoner of war camps and become hostages?
The headlines will scream that China has beaten the USA.
And afterwards, most of the Japanese Home Islands are within range of Chinese A2AD forces operating in South Korea.
We would probably see a titanic struggle along the lines of the Napoleonic Wars, where French Army (China) was supreme on land, whilst the British Navy (USA) was supreme on the seas.
It's worth spending some time looking at the Napoleonic Wars and seeing how alliances cracked, neutrality was ignored, and former allies turned on each other.
It's also worth considering if China loses. Then we're looking at a re-run of Imperial Germany capitulating and the rise of Hitler who channelled the people's desire for vengeance.
But consider that this. The US was economically 3x bigger than Nazi Germany. In comparison, it is China that could be economically 3x bigger than the USA.
To repeat again, US Admirals are far too gung-ho about the US winning a war against China.