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From the asymmetry you posit, the situation does have to look unsolvable (not in the sense that men can never get sex, but in the sense that they'll always have to make a bigger effort for it; and not through the mischievous wiles of women, but simply because of hormonal differences, very much like women apparently will never be able to compete with men in the Olympics, unless we start manipulating our genes on this respect).
The vast majority of the worlds population probably doesn't really live, at least not fully,
in what a middle class person in an advanced country would consider the modern world.
In my own personal experience, the thought you express here is 100% correct.
I'll bet most women against pornography/prostitution are e.g. also pro-lifers.
I'd like to know the answer to that too, it certainly seems like it isn't true, or at least hasn't been true in the past, of the high profile public speakers on the subject. It's true that that isn't necessarily a good guide to who thinks what.
Maybe it was the case that the public speakers you refer to were a few but spoke quite often and were believed to represent a general opinion without any real questioning of the base having taken place? (I was in America in the '90s, till 1999, so I can't talk about what happened before that from personal experience.)