Why were the Rightly Guided Caliphs specifically designated as the Four, to the exclusion of others like Al-Hasan and Mu'awiyah?

The caliphate of Al-Hasan ibn Ali (may Allah be pleased with them both), despite its short duration, was a rightly-guided caliphate or a caliphate of prophethood. It completed the period specified by the Prophet (peace and blessings be upon him) for the caliphate of prophethood, as he said: "The caliphate of prophethood will be thirty years, then Allah will give His dominion to whom He wills." The thirty years were completed with Al-Hasan's caliphate, thus his caliphate was explicitly designated and occurred by consensus.