Why does the Torah promise protection from becoming cruel specifically after destroying an idolatrous city, and not after every court-imposed death penalty?

This source-based Torah study examines: Why does the Torah promise protection from becoming cruel specifically after destroying an idolatrous city, and not after every court-imposed death penalty? It follows the canonical Hebrew discussion and the classical sources cited there, preserving the distinctions and review status of the original. This localized layer is for study and discovery only; it is not practical halakhic, medical, legal, scientific, safety or pastoral advice.