The CCP are typical bureaucratic Marxists. Decisions are collective and they are analyzed from every angle and for the message it sends.
Kim is a threat to their own stability. They want a buffer state between them and Japan/USA, and under no circumstances want a united Korea aligned with the USA. but Kim has become a real liability, and simply his nukes, on China’s borders, are a threat.
Expect Kim to eventually be killed in a coup. China will be there to help his successors
I agree with your analysis.