There are many good economic reasons to have multi-generational (at least 3 generations) households. There are some good social reasons too. There can be interpersonal benefits but also annoyances (which I think is why they decreased – plus we could afford it, the USA was living extremely richly).
This represents a significant trend reversal. Starting right after World War II, the extended family household fell out of favor with the American public. In 1940, about a quarter of the population lived in one; by 1980, just 12% did. A range of demographic factors likely contributed to this decline, among them the rapid growth of the nuclear-family-centered suburbs; the decline in the share of immigrants in the population; and the sharp rise in the health and economic well-being of adults ages 65 and older.
Another factor has been the big wave of immigration, dominated by Latin Americans and Asians, that began around 1970. Like their European counterparts from earlier centuries, these modern immigrants are far more inclined than native-born Americans to live in multi-generational family households.
However, the trend reversal has also played out among native-born Americans. And for all groups, the move into multi-generational family households has accelerated during the Great Recession that began at the end of 2007.
The percentage of the population in such households now is 16%, still significantly below the high of 24.7% in 1940.