Yippee : "And then men worked hard to try to protect the advantages they had provided themselves."
I think life is more complicated than that. It's true that male dominated societies have always been interested in controlling female mating, if they can. But they have been interested in controlling male mating too. Because the real war is between everyone and everyone as to whose descendants are going to make it into the next round of the game. Traditional male dominated societies do not exist to allow all men to oppress all women. They exist to allow powerful men to dominate everyone else, men and women. And the only reason it's powerful men, rather than a powerful man, is that it's really difficult for one man to acquire absolute power. Hence you have to make alliances.
Note that the Duchess of Wherever was always just as keen as her Duke, that their daughter should not mate with the under gardener. The Duchess has exactly the same interest as the Duke in channelling her daughter's reproductive energies towards high status males. And exactly the same interest as the Duke in seeing that her son gets to sow some wild oats.
The point of social structure is that I should be in charge and that everyone should do what I say. Everyone doesn't mean women. It means everyone. I am forced to negotiate down from there to whatever is practical.
"Remember it's only 100 years since men decided to grant some women the vote"
And remember that in the previous 100 years, the small group of men who held power were forced bit by bit and through gritted teeth to hand out votes to other men. It's not a men oppress women thing. It's a those with power oppress those who aren't for as long as they can get away with it. (Mediated to some extent by ethical considerations. So for the most part the powerful men who reluctantly ceded votes to wider classes of voters did not do so because they were defeated in a contest of violence, but because enough of their group weakened and succumbed to argument.)
Obviously the reason for the political elite being male is violence. Women can't compete in a hierarchy determined by violence. Of course the male hierarchy hasn't been about pure power for eons - the brains to plan and organise and the talent for persuasion have allowed clever persuaders and planners to dominate big thugs. But a clever persuader without the practical capacity for violence is impotent. And that's what a clever woman would be in the male hierarchy until very recently. So it's no surprise that monarchies, oligarchies and elites have been very male up till recently. But they're not about doing women down. They're about doing down everybody who isn't in the ruling club.
I am aware of occasional exceptions to the rule of a male elite - eg Greek societies worshipping Mother Nature. But there are good reasons for why such societies might have appealed to our curious species. The mystery of where babies come from is a deep one, and those who control that mystery must be in tune with the Gods. But since those societies ultimately depended for their survival on male military violence, it's not surprising that matriarchies were subsumed by patriarchies.