No, females decide procreation in male dominated cultures when males restrain themselves (which is the patriarchy of the last several hundred years). Otherwise, males pick who they fuck, even in matriarchy.
Using very loosely generated Game terminology, alphas are the top 10-20% of males, which most other males will follow the lead on, and which women will find most appealing - a breakdown which science supports.
They don't envy women. They envy the men that "develop value" without the same measure of effort. What you're reading is written by a beta who has merely regurgitated the writings of women with penis envy. He is so emasculated he confuses their penis envy with his envy of the penis of an alpha.
Women can't reproduce without men, and men can't reproduce without women. It's a reciprocal relationship specifically limited to genetic transfer. However, men do everything else of a physical nature more easily/efficiently, as a group, than women do as a group. Modernity has not made women better at anything, it's merely provided an astonishing number of handicaps, erasing many of the visible manifestations and rewards of masculine advantage in the physical realm. As women have pettily trumpeted the change in disposition, they have lost much of what they really desire, which is the masculine counterweight (or yang, as you would like to understand it). Men simply do not need women for anything other than gene transmission, and so you get the MGTOW movement, while women need men for pretty much everything else (welfare requires men, with guns).
What makes them top, and what's the science that supports it? What does top even mean? How much they enjoy themselves, their social status within a certain sphere, their psychological stability, physical health, financial stability, surveys of what women think "top" means?
Funnily enough, he talks a bit about how insecure males need to find reasons they are "better" than one another. I don't know anything about the guy that wrote the book. It's called Eve's Seed.
It focuses on the transition from Pleistocene hunting and gathering to civilization. Obviously men pick who they fuck, but the final choice that makes it all happen is female. This is what makes some men insecure (that they can decide to fuck and get nothing while women decide and always get a baby) and why they take the choice away from women which was more common in more ancient societies.
I don't agree with everything the guy says, but I'm not about to attribute it to whatever beta stuff since he trashes the thinking that anyone is "better" than anyone else. One quote from the book is something like "real men don't concern themselves with what makes them real men to other people."
The points you made about the necessity of men I find solid, but I don't see how the fact that women can have penis envy cancels out men having womb envy. I think both exist.
By the way, yang is not a concept that applies much here. It's associated with masculinity, but it's part of a broader metaphysical idea that reality is the intertwining of opposing forces that manifest in different ways on all kinds of levels. Basically, for reality to exist, there must be coherence and continuity, like how in a hydrogen atom, the electron revolves around the proton. It's a repetitive state. But with all things repeating, there is no growth or progress, like stars forming and condensing hydrogen into heavier elements. Without change, there is no reality, but without continuity, there is no reality, either. This (like a lot of Eastern philosophies) is not meant to be something to think about, but a way to look at what's already there. Taosim attempts to describe all reality in a broad way that's can't really be put into words (same as how you can't describe wetness to someone that hasn't felt it).
Are you suggesting that men in this current society get to choose what women they get to procreate with and not women?
I'm not talking about modern society, really. More the transitional period from the Pleistocene to civilization.