And as soon as the royal power was firmly in his hand, he struck down his servants who had struck down the king his father. But he did not put to death the children of the murderers, according to what is written in the Book of the Law of Moses, where YHWH commanded, “Fathers shall not be put to death because of their children, nor shall children be put to death because of their fathers. But each one shall die for his own sin.”
2 Kings 14:5-6

This wasn't politically expedient, but it was in accordance with God's Torah. Does this mean it was the right thing to do? Was Amaziah being overly legalistic in his application of Torah? These weren't everyday murderers, but regicides. Maybe their children would be grateful for the king's mercy or maybe they would try to take vengeance.