Any economic analyses based on measurements of household income (as opposed to personal income) are meaningless. The single biggest factor in the stagnation of household income in lower-income groups has been the decline in size of U.S. households. Low-income households today are far more likely to be headed by a single parent than middle-income or upper-income households. And low-income households today are far more likely to be headed by a single parent than low-income households 25 years ago.
So the problem with stagnating income among these groups is not so much an economic issue as it is a social/behavioral issue.
Socialists love artificial statistics because they allow them to ignore real world observations. "Poor" people in the US tend to own cars, refrigerators, microwaves, entertainment systems, computers, etc., and live in heated apartments or houses. In Africa and Asia, "poor" people fight over scraps of food and live in mud huts. And there are many millions of them because their governments are dictatorships and their economies are socialist.
This statement is simply false, if we measure "inequality" as we should -- among individuals rather than among the average income in various countries. The latter method means that a tiny country where the average income has declined is weighed the same as gigantic China or India. The absolute number of people in the worst poverty (one dollar a day) peaked in 1980, and has been declining since; the percentage of people in the worst poverty has been declining for even longer. Individual income inequality -- measured by what economists call the Gini coefficient -- had been rising since the beginning of the Industrial Revolution, for the same reason that inequality in distance traveled rises at the beginning of a race before declining to zero at the end. The global Gini coefficient (which rises as inequality rises) reached its peak around 1970; it has been declining since. The combination of rising average income and declining global inequality is one we have never seen in human history, and it coincides quite nicely with the globalization era.
So the problem with stagnating income among these groups is not so much an economic issue as it is a social/behavioral issue.
You are right here, and you can add to that that many households are now single people with no children at all, people who used to live with their parents. That they can afford to live alone now is also part of the story. "Household income" is one of the least informative statistics the government publishes.
A final issue that as far as I know no one has studied is what Herrnstein and Murray notoriously called "cognitive stratification" -- the increasing tendency of people to mate with people very close to them in the cognitive distribution. Presumably, the more this occurs, the greater income inequality among their offspring will be. This may be a part, even a big part, of increasing income equality, not just in the US but in most industrial societies, but AFAIK (which, admittedly, is not very F) the literature never standardizes for this effect.
I see where you're coming from, but the ratio between the income growth quoted for the top 1% and the bottom 20% is over 19 to one, and I doubt that rich households have 19 times as many people as poor households.
Twenty-five years ago you were more likely to find households with one wage earner, now for most people in most areas, its commonly accepted that it takes two wage earners to support a family.