I thought this was pretty interesting and would like to know more. (I'm a native U.S. speaker).
"Why Do People In Old Movies Talk Weird?"
This short talk mentions a phrase I'd never heard before, "Trans-Atlantic" or "Mid-Atlantic accent." He says people in the U.S. learned it in upper-class boarding schools in New England. It is, in fact, what I knew as the "Harvard accent." You can also hear it clearly in Cole Porter's (Yale) own singing of his own song, "You're the Top:"
Rolled R's--except when they are dropped at the end of words; heavily aspirated T's, and all.
It's called "Mid-Atlantic" because it's in-between U.S. and British speech.
He says Hollywood loved it, presumably because it made it easier to sell movies in both U.S. and British markets, and he mentions a theory that this accent sounded better over early radio loudspeakers. That doesn't explain to me why it was taught in prep schools, or why it "fell out of favor after World War II."
"I've never heard someone speak like this in any modern media: https://www.youtube.com/watch?v=nRp2u8d7lrg Do you think this is the mid-Atlantic accent? It sounds American to me; but like I said, I've only ever heard that particular accent in old recordings."
That does NOT sound like the "mid-Atlantic accent" to me. The Cole Porter clip I posted does. The clip you posted--with the voice pitch dropping the interval of a musical fifth at the end of every sentence--is the normal style of delivery and intonation in "announcements," the sound of "authority." It lasted well into the 1950s and into the 1960s.
In my personal experience, there were two big markers of change. The first was the extremely popular radio personality Arthur Godfrey, who used a normal conversational tone of voice instead of a radio announcer's voice. The other was gradual, but the extremely influential TV news anchor Walter Cronkite was much more conversational than, say, Edward R. Murrow, and had a style of delivery close to that used by modern newscasters.
To me, the mark of what I called the "Harvard accent"--which did still exist but was dying out when I went to college (MIT!) in the 1960s--was the occasional rolled R; the "ah" vowel where U.S. speakers would use... sorry, don't know how how to represent the phonetically... "I loffed" instead of "I laffed;" and the dropped R's at the end of words. I think it was really a prep-school accent and not a Harvard accent.
There's at least one audio recording of Teddy Roosevelt:
It sounds "odd" to me but it sounds neither British, American, "Mid-Atlantic," nor "Harvard." Some of the r's sound unusual to me, but I can't say what I am hearing--I don't hear them as "rolled." He does drop them at the end of words. There is something going on in the r in Americans at about 3:07, maybe a one-flap trill like a Spanish single-r.
This recording of Woodrow Wilson is described in some of the YouTube comments as "Transatlantic" but it sounds more U.S. than British to me; what do you think?
I came across this in a biography of Teddy Roosevelt:
'He fit in at Harvard, which was an upper-class institution. His speech, with a broad a and softly trilled r, showed that he was part of the elite of the Eastern seaboard, which showed a distinct culture of speech, language, education and behavior.'
This would have been the 1870s, so well before your time...
"Would this have been some kind of affectation?" Well, I certainly thought it was!
My memories may not be correct. They may not have done it in normal speech, but only when declaiming... you certainly can here Cole Porter doing it in the clip I referenced, but he is of course singing.
I've never come across a single person who rolled their 'r's in 'real life'. In fact, I've just spent a while listening to early recordings of the Queen and other aristocrats in the mid-twentieth century just to be sure - and no, their 'r's were perfectly normal ones. Not a trill in sight.
In fact, the rolled 'r' is a purely theatrical feature. British actors of a certain generation would use the rolled 'r' when acting, but off-stage they would speak with he same 'r' as everyone else. This becomes clear when we listen to the pronunciation of, say, Gielgud or Olivier in performances, and compare this to how they spoke with their 'own' voices in interviews. Nobody trilled in normal speech.
I'm therefore as curious as you are about why the Harvard accent of an earlier time should have a 'rolled' r. Would this have been some kind of affectation?