I specifically defined that basic value as so basic, even religious conservatives take it for granted, not something controversial. If it is controversial, it isn't a basic value. Neither Roman Catholics nor fundamentalists believe women should not interact with unrelated men, in public or private space. Men and women have interacted in "church socials", country dances, banquets and dinner parties, the market, etc. for the last 2000 years. No one argues about this, no political parties have fought elections over it or debated it in Parliament, etc.

In order to get to a place where abortion rights can even be argued, we had to have a society in which women were interacting with men in society as a matter of course.

The notion they shouldn't is to prevent any possibility of "illicit sex" happening in the first place.

And although I never claimed we are "swamped", numbers is a different issue.