"Historians" have been making a profession of misinterpreting the role of family structure for the past 30 or so years. Ditto your observation on the Southern family. Actually, the similarity to middle and planter class antebellum Southern families is striking.
This is one of the things that is perenially misunderstood about both Southern and Roman families! You didn't have to be wealthy (vide Cicero, thanks Burkeman) to have extended family in the house. For one thing, there were no "labor saving devices" and even poor households had a servant or two (just look at Victorian England. Even the very poor family, living on a pension, that took Kipling in as a child boarder had a maid.) For another, the pater familias (as part of his authority) was expected to provide for all the poor relations (you can see the same thing in Victorian England with the maiden aunts and the "gentlewomen in distressed circumstances".)
Sometimes we forget how our technology has changed civilization in very basic ways. As C.S. Lewis said in The Discarded Image (about this very issue - the difference between the medieval worldview and our own), it's the assumptions that everyone makes that tend to be overlooked when reading about another era.