The dialect you reference, the mid-atlantic or transatlantic dialect https://en.wikipedia.org/wiki/Mid-Atlantic_accent was actually taught to actors during the early years of movie history as film transitioned from silent pictures to the "talkies".
But as time went by, a new era of acting and accents, less apparently studied, more real, and striving to emulate life and its gritty actuality, was ushered in by a school of actors that were departing from the old traditions, including Marlon Brando, James Dean, Montgomery Clift - all Method actors, who were favoring a more vernacular, slangy style.
So during the 40s to 60s we actually encounter a waning of the popularity of this kind of affective speech. (According to the wiki cited above, Bill Labov, a University of Pennsylvania linguist, dates the decline of this mid-atlantic accent to as early as 1941.) Certainly, by the time the 50s roll around, actors are more and more starting to try to adopt a more low key and less melodramatic approach to scene building, playing things off with a decided cool. So the era of 1940 to 1960 was certainly an era of great flux and change in movie acting.
And even if we are to discount all the influence of the Method School in the 50s, it is still hard to lump the period of 40s to 60s into one like era. Yes, theatrical acting dominated movies in their earliest period, but there were always outlier examples that differed from the mainstream: Humphrey Bogart certainly was talking tough years before in Casablanca, even if Ingrid Bergman wasn't. And, furthermore, movies themselves from this span of 40s to 60s can be so different: compare for example 1940 film "The Grapes of Wrath" to the 1952 film "High Noon" to the 1957 film "Bridge on the River Kwai". All totally different styles. Ford's "Grapes of Wrath", though filmed in 1940, doesn't really dilly dally about with the transatlantic accent; it is gritty and slangy before Method Acting made this famous.
So here's what I really think. Yes, there are a ton of those movies with the "dahlings" and "won't you be a dear", and they comprise the fiber of that similar speech you are referencing during this period. But what is even more consistent about sound during this period of time is that movie sound technology, though it was evolving during this time, was still prehistoric compared to the advanced digital sound recording we have today. (Foley editing was around since 1914, during radio years. So it was nothing new.)
It was, in fact, the quality of the recorded sound itself that made everything sound less dimensional. The years of 1945 to 1975 are referred to as the magnetic era of sound recording (http://museumofmagneticsoundrecording.org/Magnetic.html). Analog recordings have tape hiss, and that is a background sound that is consistently there during the period you reference, and was even present to some extent afterwards, regardless of advances in analog recording equipment that came about during the 60s. Yes, some people actually prefer the warm analog sounds of yesteryear. But most ears are attuned to the layering and all the great movie magic that goes into digital sound recording and digital effects supplied by computers today.