Voted up because I like the attitude you show in your first two paragraphs.

However I think that you misunderstand the claims that you argue against.

Men have lower chances of having any kids than women

The obeservation underlying this is that that the average person has three times as many female as male ancestors. But every child has one male and one female parent. So the average male ancestor of now living people must have three times as many decendants as the average female ditto.

This might be because genocides were carried out by killing all men in a population, so that the women were forced to marry the conquerors. Or because two thirds of males that were born in some era were killed as children. Or because there was a tradition were some men killed other men's children, so that the surviving children had fewer fathers than the children that were born.

But in any case there was something going on that is not caught by your statistics. And the simplest (and nicest) explanation is probably that women got to choose who they had sex with, and some men were more attractive than others.

So why does your statistics say differently? I see two explanations off the top of my head. 1) Marriage, or in other words rationing of partners. Today each man marries one woman, and then other women are expected to marry another man and have at least one child with their husband. 2) Contraception, people have fewer children when they don't want children nowadays.

Also, I expect that if that study would talk about biological fathers rather than social fathers you would get different results.

Richer people, especially men, are more likely to have kids, and have more kids

• Rich and rational people have as many children as they want, not as many as they would have had in the past.
• See above about marriage. When many women could have the same man without being shamed more attractive men would have more children relative to others. Rich men are ceteris paribus more attractive than others, and that difference was probably bigger when normalcy for both men and women were on the limit of starvation
• The "poverty line" is not really relevant in an evolutionary context. Being "above the poverty line" in America today means being inconceivably wealthy in the terms that were normal 200 years or more ago. Genetically we have not changed much in a couple of centuries.
• Wealth in the modern sense is not really relevant either. The kind of property that would count in your survey has not been around long enough to make any significant changes to the human genome.