This is a highly cultural phenomenon those which one can not generalize about. Nordic countries have low level of poverty AND marriage. But Nordic societies are much more accommodating towards such a situation, and so it doesn't cause the significant problems it does in the US. Laws and regulations make it much easier for mothers to have a job and raise kids. In the US the workplace is less accommodating and so many mothers are forced to stay home for years with their kids. This creates an economic disaster if the parents divorce because the mother now has too little work experience to get a good job and there are limited social programs for single mothers.
Secondly a factor is the nature behind the split up. Single parent households does not signal family breakdown in the same manner as it does in the US. Fathers are usually very active participants in their children lives even if they are divorced.
I think the lesson American are trying to push is that people must be married for the benefit of children, while Nordic countries rather push the idea that every father has to take responsibility and engage with their children.
I think one should accept realities of modern societies and find solutions to that rather than dreaming about a 1950s world which is never coming back.