Uh, men want to "put their dick in you" because they want children, even if they might not be aware of it - that's nature's trick. So maybe your vagina has bargaining power, but that's only because there is a womb behind it. I guess men pay for fake plastic vaginas, but not a lot (I don't know, but probably < 100$? That wouldn't be enough for a women to live on for an extended period of time) - that is an indicator of the worth of vaginas vs wombs...
Does poverty overwhelm single women, or married women? You have to trade well... Can't really comment on the poverty issue of women and children in the US. In my country, technically child support goes to the children, not the mother, which leads to technically (on paper) some mothers having not a lot money. I think they can use their children's money to pay for housing, food and other things, so I am not sure how poor they really are.
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Edit: HN doesn't let me write more comments, so here is my reply to Mz's comment below:
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Your observations about male desires and behavior only support my point: if men would call the shots, would you expect many long term relationships and marriages? My claim is women control procreation and get to make demands in exchange. That claim is consistent with your observation of male behavior.
The story is of course oversimplified (this is just an internet comments forum): of course men have some value, sometimes. As your poverty example shows, men are helpful in providing for women and children via their work power. There are some "markets" where the power dynamics are reversed. For example I remember an article about places in the US where most black men are in jail, so the few eligible non-jailed men are in high demand. And as expected, they are not very willing to settle down. There also was that recent story in Vanity fair about men on Tinder in New York, with the same power dynamics, but I thought that article was rather low quality.
Women have their own desires - they would like to not put all eggs into one basket and have kids with multiple men (genetic diversity, better chances). That is why supposedly one in five children are cuckoo children (which I myself find very hard to believe, but I have read that several times). It's also why women don't signal strongly when they can get pregnant and get impregnated inside of the body, so that men can't be sure who is the father of the kids - and that's also why we want sex all the time, not just during periods of fertility.
As for the poverty, how exactly does it work, where do the men go? Either they are poor as well, or they are dead, or left the country? In my country fathers have to give everything they earn except for a minimum to their kids if they are liable for child support. Maybe it demotivates some of them so they stop earning money, that might be a possibility.