“Companies decided they'd just rather pay people less“

That doesn’t happen in a vacuum. Women flooded occupations they already were predisposed to, which lowered their wages. They also flooded all kinds of office work which reduced those wages too. Then those steel mills & factories you mentioned suddenly had back offices (before computers) filled with women to handle the paperwork in air conditioned offices. Wages gains disappeared in the 70s due to this influx and resulting inflation of all these new salaries. Same old case of too many workers and not enough jobs.