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.

All diversity efforts that I've ever seen are the exactly opposite of profitable and result in sexist/racist/otherist selection of candidates. The unfortunate end result of worse selection is that worse candidates were hired.. every. time.

Why wouldn't a company want to target groups that other people are missing? It means that you can get good candidates for cheap.

Obviously you don't lower the bar. You kept the hiring bar exactly the same, but get more people from certain groups to apply.

IE, if you can find someone who passes your hiring bar, but no other company has noticed, that means a cheap candidate.

If you target the group that everyone else is going after, they are going to be much more expensive for a given quality level.