A messiah was sent with the specific purpose of saving humanity from their sins, but unfortunately failed to overcome his human weaknesses. He was said to have an " impatient eye " with the opposite sex and succumbed to his lecherous instincts. This led to demigods being born all over the ancient world, numbering in the hundreds. These demigods were considered superhuman, with abilities far outstripping the capabilities of mortals. They would go on to perform great deeds, such as slaying monsters plaguing the world, or sacking great kingdoms for their nations. Their deeds would inspire many myths and stories about their adventures and conquests, provoking the envy of mortals and inspiring others to live up to their legendary reputations.
Gods are considered to be enhanced humans, not only in body but in mind. Every emotion they feel is magnified ten fold, such as love and anger, which led to their dramatic behavior and over-reactions that many of them displayed in myths of the past. Their offspring would naturally possess these qualities, albeit on a lower level than their parents. This is demonstrated in the ancient myths from their overly cruel punishments of mortals to their heroism and fearlessness in battle against monsters. As their egotistical and charismatic behavior is directly linked to their accomplished feats, it isn't that far of a step to desire actual political power as well. The ancient world was a time of might makes right, and the strongest of individuals would naturally seek to dominate others and rule kingdoms. Many kings started out as warlords who conquered some territory and expanded their power base. Demigods could certainly gain the support of the public and would easily overthrow lesser mortals in a struggle for power, seeing as how the ancient world valued the characteristics that they possess.
Demigods allowing lesser mortals to lord over them seems opposed to their nature. How can I make this scenario more likely to occur?