When Moses turned to the tribe of Levi, his command was not simple slaughter. Targum Pseudo-Jonathan, the Aramaic paraphrase of the Torah, preserves the full instruction, and it is stranger than the plain text suggests.
"Whosoever has sacrificed to the idols of the Gentiles, let him be slain with the sword. And now, go, pass through from the gate of the sanhedrin to the gate of the house of judgment, in the camp, and with prayer before the Lord that He will forgive you this sin, take vengeance upon the wicked workers of strange worship" (Exodus 32:27).
Notice the three movements. First, a legal verdict delivered at the sanhedrin gate. Second, a march through the camp from one gate of judgment to another. Third, and this is the detail the Targum alone preserves, tefillah, prayer on the lips of the Levites as they walked. They were not to kill in rage. They were to kill in grief, asking God to forgive what their swords were about to do.
The beit din acted. But the Targum refuses to let it be cold. Even in a moment of necessary severity, prayer accompanied every step. The Levites were priests in training, and their first priestly act was weeping before the Lord while judgment was executed.
Takeaway: Justice in the Jewish imagination is never executed without prayer. To enforce without weeping is to stop being a Levite.