The President exercising command and supervision over the CMSA is grounds for impeachment

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Constitution Article 66, Paragraph 4: "Executive power shall be vested in the Government, the President as Head of State."
Constitution Article 75 and Articles 86/87: The President shall oversee and direct the various executive branches through the Prime Minister and "the Ministers of each Ministry."
Government Organization Act Article 7 (Command and Supervision Rights of Heads of Administrative Agencies): Ministers of each Ministry shall command and supervise the heads of external agencies (National Police Agency, CMSA, etc.) under their jurisdiction.
Legally, the President cannot directly command or supervise the CMSA..
The CMSA is not just an ordinary government department; it is an investigative agency that must strictly maintain investigative neutrality from undue political pressure. Therefore, direct command and supervision by the President is strictly prohibited by law.
The President directly commanding and supervising the CMSA? That is exactly what constitutes grounds for impeachment.