It's not peculiarly American, it's a Western European, especially Northwestern European, pattern. See https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2917824/, particularly the multigenerational household columns in the various tables.[1] And I'd bet it's related to the phenomenon of late marriage that has historically distinguished Western Europe from most of the rest of the world for the past 500 years: https://en.wikipedia.org/wiki/Hajnal_line

I'm tempted to admit that the expression of this otherwise shared culture might be intensified by some of the more distinctive aspects of American culture (e.g. pioneer spirit, as mentioned elsethread), but I hesitate because assuming America is exceptional is a bad habit I'm trying to kick =)

[1] That paper is something of a rebuttal to the argument that NW European culture (including North American culture) was always strongly nuclear. But the lack of multigenerational living seems pretty clear; what they seem to show instead is that the trend of the elderly living alone is relatively new. Which doesn't seem surprising. A culture that pressures children to move out of the home doesn't imply a culture that pressures the elderly to live alone.