Have people systematically studied the structure, function, composition of the private family dinner in American history (particularly 20th century, but I'm not at all picky)? I'm guessing the answer is yes, given the pure volume of historical research that occurs, but I know nothing about how that work would be done or what results it would uncover. So I have a few questions.
How does one go about studying a phenomenon that's both private and ephemeral? My first thought was surveys, but that only gets at contemporary practice, so unless someone started doing that fifty years ago, it's not much use yet, on this subreddit anyway. Unlike the study of the structure of family homes (for example), there's not much physical evidence remaining. And diaries and the like would give very scant sampling that seems more up my (medieval) alley than the standards expected of modern history. I guess there are business records, e.g. from grocery stores/consumables companies. That'd be a start, anyway.
What do we know about the function of the family meal over time? I think it's fair to say that meals have always tended to be bonding, communal experiences--has that been consistent throughout American history? Did any of the social movements (Great Awakening, hippies, anything of that sort) affect how Americans saw the value of evening meals as a family (slash other evening activities, I suppose)?
What do we know about the details of family meals over time? Do we have statistics regarding the types of foods eaten (finger foods vs. those requiring silverware, homemade vs. grocery-bought vs. take-out, etc.)? What about the location of the meal--e.g. is there evidence of a distinct shift from the 1950s (with a picture in my mind of the Cleavers around a table, as oversimplified as I know that conception is) to the 70s and 80s, as televisions and microwaves (and therefore TV dinners) become common household fixtures?
Those are the questions on my mind, but I'd appreciate any knowledge you can drop regarding private culinary culture in the US.
Actually I do know about some books that cover this, but you need to come at it sideways a bit -- food history is often a big part of women's history, so welcome to the gender history department! ;)
The books I've read draw on a variety of sources to reconstruct average home life in America, often used are cookbooks and home management manuals. Personal letters, census snapshots of women's employment, and various government reports on the welfare of the poor also have their place. Have a poke around Cornell's HEARTH collection and Feeding America for the sorts of primary sources used. Hathitrust and Archive.org also have a good amount of old home economics books. I find "economical" themed cookbooks the best grasp of what people were probably actually eating in a lot of instances.
Never Done: A History of American Housework by Susan Strasser, 1982, this books has been republished a couple of times as it's quite good
Just a Housewife: The Rise and Fall of Domesticity in America by Glenna Matthews, 1989
More Work for Mother: The Ironies of Household Technology from the Open Hearth to the Microwave by Ruth Schwartz Cowan, 1983 (I think this one has some discussion of your "where we eat" question but I don't remember!)
There's also some interesting work with immigrant communities in America and how they used traditional foods to maintain their identity. Struggling to think of any off the top of my head but most books about the history of Italian cuisine will cover Italian-American food and identity in the 19th-20th centuries. Of all the ethnic identity markers in America food is the one that tends to tough it out the longest against assimilation, and a few German food vestiges are about the only thing left of the immigration patterns in my particular area of America.
One thing you left out of the bullet points -- you didn't mention the shift in time you ate dinner in America! My grandparents still eat their biggest meal, which they call dinner, at noon, and they eat supper at night which is a smaller meal. This goes back to old-country patterns, especially if you look at the traditional meal timing in Germany. The structure of modern work doesn't allow for a big noon meal like farm work did, so the dinner/supper pattern is almost entirely lost now.
There was a pretty interesting project that began in 1935 under the Works Progress Administration called the Historical Records Survey. Part of it was an investigation of current American culinary practices called America Eats. Mark Kurlansky's book The Food of a Younger Land and Pat Willard's book America Eats!: On the Road with the WPA both give an overview of this topic, and I believe the originals are available in Washington. The study wasn't really scientific or comprehensive, as writers were sent to an area and just reported what they found. As such, a variety of eating practices were reported on, ranging from family meals to communal gatherings of all types. I don't have either book at hand, but I recall at least some discussion of smaller gatherings in each book. I heartily recommend both books, especially Kurlansky's (a favorite author of mine).