A minority of those single men have numerous (sometimes >hundreds) short-term relationships. But far more of those single men have very few or even no relationships at all. I think this disparity is far more extreme for men than for women.

If that upper echelon of single and promiscuous men were socially pressured to stop man-whoring and settle into healthy long-term relationships, then the rest would have better odds. Of course those men will never voluntarily change their ways unless there exists a strong social pressure to change. In the past, this pressure existed in the form of men without partners [wives, but it doesn't have to be wives] being viewed with suspicion if they wanted to attain social standing at work or in their community. This pressure has all-but evaporated into nothingness.