If women were paid less than men, why aren't there women-only staffed businesses dominating markets due to less cost for production/services?
The statement is that “women make x¢ on the dollar that men make.
You can “explain away” much of the gender gap by accounting for all sorts of things like career choices, aggressiveness of switching jobs and seeking promotions, experience levels, etc.. But that doesn’t make the problem go away or those things not issues unto themselves.
One of the factors you control for is job title. When you only compare people with the same title the wage gap shrinks a bit. For some reason people interpret this as "Great! Not a problem. Moving on." when it completely ignores that as a group women holding lower paying job titles is itself indicative of a problem -- career paths that are dominated by women are seen as less valuable and girls are socially pressured away from more lucrative careers (you know like software engineering where every woman in our field including myself can tell you stories of being the only girl in her class) by parents, academic advisors, the school and workplace culture the fields cultivate and pushed into "softer", "more nurturing", "more creative" career paths compared to boys.
Which it itself a problem for boys because boys who want to go into things like art, music, design, writing, fashion, social work, are mercilessly pressured away from it where girls are more likely to be encouraged. The patriarchy hurts everyone folks.
In general men are more likely to value social status because a man with a high career title is more attractive to women, whereas a woman's title does not increase her ability to find a husband.
In fact, women by and large prefer men to have a higher career title than themselves. Is it any surprise men want to climb the ladder more.
Just look at the charts. Honestly, failure to understand this simple aspect of human nature is the reason for a lot of social ill, ranging from 'incels' to the disastrous egalitarian social policies.
The second study (with a smaller but believed to be more representative sample) asked slightly different questions, and concluded that there was some statistical significance on "Makes at least as much money as I do" and "Has a successful career," which don't by themselves support the hypothesis that "women by and large prefer men to have a higher career title than themselves" (though I can agree that it waggles its eyebrows and points in that direction; perhaps suggesting follow-up studies).
Most people across the world wouldn't raise their eyebrows, since such claims are pretty much universal throughout most civilizations.
The [citation needed] for that is the stuff of multiple lifetimes of research.
(For example, when the citation was provided on the claim a few layers upthread, it indeed was revealed to be wanting, as the bulk of its data relied on Internet polls).
If you follow your thought, you would need to discriminate against the privileged group you have identified. This will cause a rift between groups that get penalized and those that get advantages, obviously.
Basic toxic middle management strategy to cause strive among your minions so that they don't pester you. This is what you are mirroring 1:1.