You insist on using per capita income for some reason. That means that even in a single earner family, the income is considered to be divided equally among the family members.
If you are a single earner making $160K in a family with two adults and two kids, then when using per capita income you consider all four family members as making $40K each. That’s the definition of per capita.
And that’s why it’s nonsense to say that per capita income of $40K is not enough to afford a house. A family of five with per capita income of $40K would be in the top 10%.
Household income is total family income, regardless of whether there is one earner or more than one. And it’s not tautological. If your household income is very low, then your family may not be able to afford to buy a house.