It may seem like this makes sense, but in most places it's the opposite. Low income women are single mothers at a higher rate than women with high salaries.

In most western countries, low income women do not become much poorer if they become single mothers. In some places, it increases their living standards. But for upper middle class families, a breakup tends to be costly.

Also, there seems to be shared causal factors that lead to both stable relationships and financial stability. Such as impulse control, mental/physical health and the ability to postpone gratification.

You don't need a house to have kids. Plenty of people don't and they do just fine. And if they're choosing to have a kid on their own, they've planned out finances, too. Fertility treatments aren't cheap.