The Turkish rulers maintained harems all the way until the end of the Ottoman empire.

Yes and they were comprised of women who weren't Turkish. So this had no negative affect on the men in the Ottoman Empire. It definitely sucked for the men in foreign lands that were subjugated by the Ottoman Empire though. They constantly had to send a percentage of their women and boys(to be raised in the Ottoman Empire and to serve as soldiers) to the Ottoman Empire as tribute. The descendants of the men who were subjugated despise the Turks to this day.

and many men having access to no women.

Yes, if they were slaves or died young otherwise there would be a collapse. And having too many slaves is not a good idea. That's why the Romans, always ensured, they didn't have too many slaves but enough.

Females, by the way, as observed, tend more towards polygamy. They would rather share one "alpha" male than be exclusive with a beta one.

Female mate selection was not like this, all the time. It was constantly changing, depending on the environment. What you are describing is just how it is, today. Because in our current environment, this is the most efficient way for them to pass on their DNA. An extreme level of gynocentrism makes women, behave that way. Any other way, would be going against their only purpose in life. So females just go for whatever works best based on their prime directive. One man for life or 100000 men for life or being in one man's harem etc. They just go with the flow...

The female biology primed her to socialize, exploit males, and get "the best seed" - even if the entire universe burns around her.

I agree. And even if she burns with the entire universe. They are just primitive baby making machines, capable of adapting to any environment. Nothing complicated and special.