If China and the US are in a naval-air war, China will lose. And desperate leaderships will do anything to avoid defeat.
And if China loses, how long will North Korea survive as it will be utterly alone? Fatty Kim knows this.
So Fatty Kim would welcome Chinese soldiers engaging the US 2nd Infantry division based in Seoul. And nothing Seoul will do can stop China seeking to engage the US on land, where it is China that has the relative advantage.
It will be a re-run of the Korean war, except China has a good chance of conquering South Korea and capturing the US 2nd Infantry division. The worse case for China is just another stalemate like last time
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.