Did you miss where I even listed all men ever mentioned in the game? There is one male political leader mentioned: the Prince of Sam'ra, and he's only mentioned in passing (and the one thing he tried to do was unsuccessful). Meanwhile, every political leader in both Aiverow and Adas are female, all heroes or political leaders other than the Prince of Sam'ra that have been mentioned by anyone in the game have been female (Victoria the Calamity Witch, Mage-Doctor Joan Torare, the Holy Maiden of the Maris Holy Queendom--also note that country's name, the 'Sky Nine-Tailed Foxess' of Isharia Clan, Calantha Vi Emberlynn, and Queen Marialis -- all female. While the gender of the Almighty Shogut of Izuma hasn't been mentioned, that's the only one of the champions we don't know the gender of. Lastly, we've got 8 Divine Dragonesses and 8 goddesses, with no gods or male dragons mentioned. That's enough for me to assume that the political structures of the world are dominated primarily by women, as expected since women there are the only ones who can use magic.
As for why they accept being dominated by a man or being in his harem, the MC specifically has powers that make them more favorably inclined towards him no matter what.
Beyond that, why would a mostly matriarchal society necessarily have to have issues with men being competent? You said that this was one of the things that confused you about the setting, but beyond stating arbitrarily that 'human nature is ugly' and that there must be prejudice when one gender has more power than another, that's just an opinion, and based on Earth. The game's world doesn't have to owe anything to Earth, and since there hasn't been any such prejudice shown, there doesn't need to be any inherent in the setting.
