That's silly. First off, most people pay to have sex, in some way, rather than expect to get paid for it. Europe has had cradle to the grave services for decades and the one constant there is the birth rate is the worst on the planet. By contrast Africa has a soaring birth rate and much of the continent is third world.
If you have to pay people to screw, you've already got much bigger problems on your hands, and social services isn't going to fix it.
Honestly, when it comes down to the brass tacks, is, any time you have a society that is sufficiently wealthy, women are going to want more out of life and raise their price for it, and men simply are not going to want to pay it, and so they don't. Seriously, if you are a guy, what would you rather do, run the risk of being the next me-too, go through a bunch of rejections, invest all this time into getting a halfway almost cool girlfriend, or even a wife, and then, when you do, run the 50-50 chance of having your life be destroyed in a divorce... or just fire up World of Warships and count your 401k earnings later on?
For younger men, the pursuit of women is just too much work and there's too much risk and no payoff. Remember, even in the days when women were basically property, you still had families paying the men to be married to them, and you expect, gosh, with less value and more bills, what is going to happen?
You can call it what you will, misogyny, whatever, but the numbers don't lie. Men are bailing on married society, if not society altogether. It's just too much of a pain for some people.