I can start off.
I'm not sure that your hypothetical actually captures what's at play here—and I understand hypotheticals are always hard to draw—with the concern with respect to market forces. The issue that led to the recognition of pay equity in the first place was the recognition that women enter the labour force with a vulnerability to gender discrimination, and the characterization of jobs as being considered typically female results in a devaluing of them. The bargaining power that women and groups of other vulnerable individuals have in entering into an employment relationship reflects discriminatory attitudes and presuppositions, and in fact is such that it's not a situation in which we can say that the market forces operate neutrally and without gender discrimination. The statistics we see about pay inequity between men and women are products of that process, so why would we go back to that process thinking it would remedy itself?