Not sure if small families will solve poverty and the pathologies associated with it since that seems to be more about how people choose to live their lives, but at this point in history with wages stagnating it sure would help. People already appear to be cutting back on the number of children they have. When I was growing up, families with 4 kids were common, now they are rare. Not sure what is going on in the underclass, where they really can't afford to have a lot of children, but never could, and are caught in the poverty trap.
People used to have a lot of kids for three primary reasons: 1) because many kids did not survive childhood diseases, so people had a lot with hopes some would survive, 2) they needed kids to help with the family business or farm, 3) they needed kids to take care of them in their later years.
Number 1) has been solved by modern medicine. Number 3) has been largely solved by government programs like Social Security and Medicare. Number 2) is less relevant since not many people make their living via farming anymore and modern technology helps with farms and small businesses in ways that were not possible generations ago.