I think you're missing the pink elephant in the room.

It's a two-part problem mostly (but of course there are several others).

First of all, China does not want the U.S. right across the border. South Korea is fine, but is heavily influenced by the U.S. North Korea is hardly a threat, with the threat being an attack on South Korea. Because of this, China does as much as it can to prevent conflict. While I agree that China could absorb the economic costs more readily than South Korea, it would not be a wise choice politically.

The second reason is more sociological: culture and identity. People often forget that North Koreans have their own culture and traditions. The government indeed has an iron grip on its citizens, but we should understand that the culture is separate, if not mixed, from the government. They will not readily give that up just to be Chinese. Plus, in the case of South Korea, if China is on the border, there will be a massive immigration problem. South Korea will be extremely upset, as most already don't have a high opinion of most Chinese. If you recall South Korea's history, they were colonized by Japan and in the process lost a lot of access to the very things that defined them as Korean. If Chinese people start flooding South Korea, there would be some serious clashes due to differences in culture in fear of losing this identity. The Chinese would not want to be Korean, and Koreans would not accept Chinese practices. This is not including the chaos that would ensue in the education system. It's not like the U.S. because the U.S. prides itself (well, at least in words) on diversity. Korea prides itself on purity and image, similar to Japan (who also is against mass immigration). This is not to say that immigration isn't possible, and Koreans certainly do tolerate and accept a mild influx of Chinese, but for a country like Korea with its strained history the idea of merging and possibly losing its identity is simply out of the question. Eventually, it might even get to the point of China saying "Hey, you have a lot of Chinese people. Why not stop being small and join our larger country?" Sounds like Taiwan a bit to me, and you can see how that turned out when Taiwan said no; they can't even be declared a country without repercussions from China.

(Note: this is what I have observed from what Korean people have told me. As an American, I am for controlled immigration but it is not my place to insist it from another country. South Koreans would be delighted to reunify with their relatives across the border, as they share a generally common language and culture, but many would disagree with doing the same with another country, especially with Japan or China.)