The following is speculative and reliant on memory, not yet citing scientific references. I feel it includes significant insight, but wouldn't mind if anyone posts evidence to the contrary.
Sex's advantage/purpose in life's evolutionary processes is not yet as simply definable as, say "it enhances genetic diversity". But obviously there are several, complexly related advantages of sex in evolution that outweigh its disadvantages, on the whole. (Recall, bacteria are still evolving, non-sexually, or at least non-bisexually.)
One of the clear modes of sexual selection employs male competition and aggression. The strongest and cleverest males pass on their genes, thereby adding to the gene pool any genes that may contribute to successful clever and/or aggressive behavior (e.g. more developed brains, antlers, musculature, and so on). Until the costs of these larger and more complex physical and behavioral features don't overburden the creature's non-sexual daily lifestyle (e.g. in energy or other resource requirements), a positive feedback loop of increasingly competitive male physique and behavior remains in play.
There is even a significant percentage of Genghis Khan DNA in a wide range of human populations, thanks to his (and his family's) legacy of raping and pillaging! And thanks to the accelerating, expansive nature of civilization.
There is also a less physically risky/harmful type of sexual competition, e.g. competition of plumage among male peacocks, lion manes, or other conspicuous displays that consume excess energy and resources, but I won't address that here.
Sexual behavior has been a significant factor in evolution of animals for millions of years, if not a half billion. But it's only in the past 50 thousand years or so that the diversity and depth of human culture has accelerated to unnatural proportions; human cultural evolution now trumps genetic evolution in its influence over our future, except perhaps in cases like how bacteria evolve to overcome the antibiotics we try to kill them with.
How significant is the competitive nature of sex in human cultural evolution, versus the competitive nature of sex in human genetic evolution? A simpler question may be, how much real choice do we have in our personal sex-base behavior, albeit as we know, it's a question that doesn't necessarily lead to simpler answers.
Now on to my main focus. I postulate that the most dynamic mode of human evolution in the past thousands of years has been cultural (as opposed to genetic), which has for better and for worse enabled and enhanced human male dominance to an unnatural and unforeseeable degree.
The unnatural degree of male dominance accelerated the growth of civilization, becoming accepted and institutionalized to the point of increasing traditional ignorance (and often even intolerance) of female perspective and influence. Our patriarch-designed male dominance over society, law and morality (also manifesting as the He in myth and scripture) has been enforced for thousands of years, by the combination of natural, genetic evolution of male physical power and aggression with the newly evolved power of intelligence/cleverness, the imposition of culture and memes, and application of aggressive idealism and religion. This (the above), simultaneous with having women at home rear children and make personal sacrifices in support of their male head of household, thus overshadowing previously respected female roles in society at large (albeit previous "society" was smaller, at more band and tribal sizes).
Uh-oh, now I'm stuck. I expected radical but feasible solutions to spew forth from my subconscious, but nay, nothing but empty space and darkness! And heaven forbid I fall down the slipper slope of blaming one sex or the other for today's evils! Can anyone out there help me, or is this just a totally useless read?