The way that it works is that you hire anyone at all who can pass the hiring bar, and then negotiate salary afterwords.

The problem is quantity. At the end of the day, if only X people that you interview pass your hiring bar, it is impossible to hire more than X. You can't just say "Lets double X!".

Now, would companies do things like try to reach out to women groups, so as to increase the amount that interview with them, and therefore increase the proportion that are hired?

Yes, absolutely they would do that. As has been demonstrated by all the diversity reachout efforts that companies are doing to women and minority groups. Diversity efforts are PROFITABLE.