By contrast healthcare is more than 3X the size of STEM, and when looking at new entrants is just as skewed towards women as STEM is to men. When you step outside STEM and healthcare, and look at high-paying jobs that actually employ at scale, you see that most of them heavily favor "soft skills". Attorneys, real estate agents, middle management, marketing, sales, speech pathology, graphic design. All of them are much more about working with people than working with things.
Ultimately the point still stands. "Cooperation and communication" are not the super valued soft skills you claim they are in the initial years, which is about the only period women outperform men in earnings. Afterwards, women are left behind in the dust as a whole.
It's blatantly obvious there's more going on here than "women are better in the post-modern labor market".
Despite the whole "cooperation and communication" argument, most individuals aren't going to be in such a position for quite a few years, where the income differences are. During those times, most individuals are stuck doing grunt work.
Call me crazy, but things don't add up here.