Europe too practiced cousin marriages more commonly until relatively recently. The Queen of England and her husband are cousin, Darwin and Einstein married their cousins.
The problem is not cousin marriages up to a point, but a weak state and what people do to insulate themselves from that weak state. If the state is stronger and more reliable, people can be independent from their families. As the economic situation of many families declines in the World and particularly the west, you see the return to multigenerational housing.
In the US the eugenics movement about a 100 years ago heavily propagandized against cousin marriages and with US influence spread throughout the World over the following decades, it was seen as the more “civilized” thing to do.