I'm a little pressed for time so I'll answer in depth later but the three biggest reasons are:
Korea was a Chinese vassal state
Their relationship changed several times throughout the centuries, sometimes warmer relations, sometimes cooler, and occasionally warfare erupted between Chinese and Korean lords but for the most part, Korea recognized Chinese hegemony of the region.
Korea pledged symbolic loyalty and allegiance to the Emperor and in return, the Emperor gave the Korean king legitimacy and political backing. This relationship was usually mutually beneficial politically, militarily and economically.
More on the warring part. One might assume that with China's size and large population from which vast levies could be drawn from, a war between China and Korea would be very one sided. But Korea is fairly mountainous and is a difficult place to wage war.
Additionally, the more massive an army grows, problems in maintaining and supplying it grow proportionally, especially when that army is sent abroad. For one soldier, you need several people to armor, arm, feed, clothe, and shelter him. This is as true today as it was hundreds of years ago.
As you can imagine, it was insanely expensive to consider military expeditions into Korea where you could expect resistance to be united and stiff.
Korea is culturally and linguistically distinct from China
While no one can argue that Korea is/was heavily influenced by Chinese literature, art, culture, religion, and language, Korea has had its own long history of distinctly Korean culture. Particularly, language is a major part of a group's identity.
While many educated Koreans throughout the centuries would have had to learn Chinese and study Chinese texts to be truly considered a scholar, Chinese language did not replace the Korean language.
Also, the Korean acceptance and command of Chinese culture helped contribute a great deal to warm relations with various Chinese dynasties. This helped Chinese lords look upon their neighbors as fellow civilized people, albeit patronizingly (in a sort of big brother-little brother "what would you do without me?" kind of way).
China has often been preoccupied with internal management
China has been, for much of its history, a massive collection of land and people. Even today, with the help of technology, managing and running China is a bureaucratic nightmare.
Depending on what time period exactly, Chinese rulers would have had to deal with constant peasant revolts, opportunistic warlords and bandits, threats of secession, bureaucratic corruption, abuses of power, scheming court officials, unruly aristocrats, droughts, starvation, plague, civil war, etc.
And of course, again depending on the time, incursions from steppe people or other 'barbarians' that encroached on China's frontiers.
With all these issues to deal with, it simply wasn't worth it to devote massive time and resources to conquer and then settle/assimilate Korea, which itself was no simple task.
In summary
Korea was more useful as a trade partner and allied vassal state than as another frontier for the empire.
Occasionally China and Korea did go to war and China certainly did not steam roll the Korean armies then. It certainly would not have been easy to conquer Korea and even if it was, China just didn't have any needs or desire to do so.