Why did the Ming and Qing dynasties accept North Korea as an appendage instead of putting it directly into the territory?

Why did the Ming and Qing dynasties accept North Korea as an appendage instead of putting it directly into the territory?
Before the Ming and Qing dynasties, the Chinese ruled the Korean Peninsula and brought North Korea into China's territory.

many people know that Korea existed as a vassal of the Chinese dynasty in the Ming and Qing dynasties. However, before the Ming and Qing dynasties, the Chinese ruled the Korean Peninsula and brought North Korea into China's territory. This origin was also recognized by Lee, the later ruler of North Korea, "in fact, the land of China, so that our country can govern it."

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