Your question has some flawed premises. The Korean pennisula was actually fully conquered several times by invaders (not necessarily by the Han Chinese themselves at the time, but more by the Mongols/Mongol-ruled Chinese or Manchus/Manchu ruled Chinese). In regards to the Han, Yuan, and Qing:

The Han Dynasty conquered Gojoseon (geographic North Korea) while geographic South Korea remained independent among the Jin Confederacy (evolving into the Jinhan Confederacy) - a loose coalition of small kingdoms and tribes. The Jin Confederacy seemed to have had good relations with or was an ally of the Han Dynasty so the Han had no political reason to conquer them. There also probably wasn't an economic justification to conquer them - similar to why the Romans didn't conquer Scotland/Caledonia. The terrain was rough (mountainous), the region was filled with unruly natives governed by many independent leaders, and the region was "relatively" poorer - so the costs of an invasion would not have been worth it.

Goryeo Korea was actually conqured by the Mongol Yuan Dynasty after the Mongols conducted multiple invasions (9 different raids and invasions with varying degrees of success) and Korea finally surrendered and became a vassal state controlled by the Yuan. Korea became independent after the Yuan Dynasty collapse. The number of Mongols in Korea and timeperiod here was too short for any type of assimilation into Mongol culture.

The Manchu led Qing did actually invade Joseon Korea twice (and ended up fully conquering them by the end of the second invasion) because Joseon supported the Han Chinese Ming Dynasty. The Later Jin/Early Qing invasion of Joseon Korea in 1627 resulted in the Qing being established as the tributary overlords over Joseon. The Qing invasion of Joseon Korea in 1636 due to Joseon's continued support of the Ming Dynasty resulted in the complete conquest of the Korean pennisula and where Joseon Korea would become a vassal of the Qing all the way up to 1895. In 1895, Japan had defeated the Qing Dynasty in the first Sino-Japanese war and made the Qing sign a treaty that made Korea independent from the Qing, and then the Japanese made Korea a part of the Japanese empire.

As for assimilation, interestingly, Korea considered themselves the true inheritors of Han Chinese culture and civilization after the Manchu ruled Qing Empire destroyed the Ming Dynasty (and the Qing then started banning Han Chinese cultural elements). So in some sense, the Koreans inherited and assimilated to traditional Han Chinese and Confucian culture while the Han Chinese themselves were forced to assimilate to Manchu culture.

So you can say Koreans did assimilate into Han Chinese culture and did so voluntarily during timeperiods such as the Ming Dynasty, and ironically around that same Ming timeperiod, the Chinese themselves were conquered and assimilated into a different Manchu-Han Chinese hybrid culture.