The Emperor of Liang had no direct administrative power, only the right to veto.
Therefore, even with the death of Prince Liang Chu, the Emperor could not directly order The Ministry of Justice and other institutions to investigate the case.
However, the Emperor could write a letter to the Prime Minister, allowing the Prime Minister to command the civil and military officials.
If the Prime Minister did not accept the Emperor's suggestion, then the Emperor might intentionally use his veto power to make things difficult for the Cabinet in future administrative and judicial matters.
"If you don't give me face, naturally I see no need to give you face"
Moreover, the death of a prince was no small matter; even without the Emperor's suggestion, the Cabinet could not simply turn a blind eye.