Why do some sects revere Sayyiduna Husayn and his sons, but not Sayyiduna Hasan and his sons?

The Shiites have restricted the Imamate to the descendants of Al-Hussein, to the exclusion of Al-Hassan. They justify this by claiming it is a divine selection, or a compensation for Al-Hussein for what befell him, or a punishment for Al-Hassan for his reconciliation with Mu'awiyah. They cite narrations to support this, such as the saying of Al-Sadiq: "Indeed, Allah, Blessed and Exalted, loved to make the tradition of Moses and Aaron flow in Al-Hassan and Al-Hussein," and his saying: "Indeed, Allah, Exalted is He, compensated Al-Hussein for his slaying by placing the Imamate in his progeny," and the saying of Ali ibn Al-Hussein: "Indeed, when Allah, Blessed and Exalted, saw what Al-Hassan did with Mu'awiyah, He refused to place the وصية (succession/trusteeship) and Imamate except in the lineage of Al-Hussein." The Sunnis, however, consider all of this to be falsehood, and they regard the belief in bada' (divine alteration of will) as kufr (disbelief). Some Sunni researchers have posited that the secret behind preferring Al-Hussein and placing the Imams among his descendants is his marriage to Shahzanan, daughter of Yazdegerd, the Persian king, who bore him Ali ibn Al-Hussein.