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Part of what is going on here is that you are assuming that characters/actors in these movies are talking/speaking like actual people on the streets. In fact, even in movies that were trying to be more 'gritty' like early film noir, etc., American actors in early sound pictures spoke almost exclusively in what is known as 'Mid-Atlantic English.' The name, which sounds as if you might be from halfway along the Eastern seaboard of the United States (Jersey, Delaware, Maryland, etc. are often called the MidAtlantic), actually refers to the fact that the way of speaking was as if you were raised on an island in the middle of the Atlantic Ocean.
Mid-Atlantic English was a conscious effort to combine the 'high-brow' and 'high-class' connotations and affectations of 'Queen's English' from the U.K. with the American accent of New England elites to craft something new. If you would like to hear a fantastic podcast featuring many examples of this accent from American movies in the 30s through 1950s, as well as Queen's English and more common-place, vernacular, American accents from the time, listen to this episode of The Allusionist called "The Evolution of Accents". For a quick clip, check out Katherine Hepburn's famous mid-Atlantic accent in Philadelphia Story -- Cary Grant also is speaking it, though! -- or any of FDR's Fireside Chats.
While lots of analysis of Mid-Atlantic English focuses on the accent itself (in the podcast I linked to, a linguist goes into fantastic detail about the importance of 'r' sounds, etc.), your question actually draws attention to the fact that this was much more than an accent -- it was an entire manner of speaking, and involved word choices, syntax, and diction that (both then and now) sound 'elevated' in certain ways. Mid Atlantic English was a cultural project to standardize 'learned' and intelligent ways of speaking that were disconnected from place: if everyone spoke with the same place-less accent, you couldn't judge them or their intelligence based on a first listen to their southern drawl, the non-rhoticity of Boston natives, the elongated 'o's of northern Minnesotans and Wisconsinites. Of course, this ambitious cultural project began and was perpetuated through many elite institutions, especially the private college preparatory schools that privileged youths like FDR could attend, and the Julliard School of NYC. Ironically then, speaking in MidAtlantic English was actually the opposite of democratizing; it instead marked you as a wealthy, well-educated, upper-crust, cultural elite. OR it marked you as someone desperately pretending that they were those things: one of the reasons Audrey Hepburn was chosen for the lead in Breakfast At Tiffany's was because her Mid Atlantic English was the perfect speech pattern that a poor country girl trying to make it big in New York City would adopt to hide her past. (See also her role in My Fair Lady -- again, the accent is crucial!!!) Scene from Breakfast At Tiffany's..
I'm not actually sure whether Rodgers mentions Mid Atlantic English, but the fantastic book Atlantic Crossings: Social Politics in a Progressive Age by Daniel T. Rodgers discusses the larger cross-oceanic cultural conversations in which this accent flourished. Elites on both sides of the pond were working to create bold new futures: some of their projects were visions for urban designs and public housing, and Mid-Atlantic English stands out as another example of a cultural project from this era with the goal of creating a more unified and just future.
Sources:
First, there are plenty of movies from the 1930s featuring less sophisticated and formal speaking. Take the gangster noirs, for example, like Public Enemy and Angels with Dirty Faces. And of course the populist classics like Make Way For Tomorrow and Of Mice and Men. There were also numerous films made by and for African Americans, and a fair number of "hayseed comedies."
But what I think you are really observing is survivor bias. Over time historical periods' representations in art and culture crystallize around their Platonic ideals. So we admire the Colosseum and not the pornographic graffiti of Pompeii, Michelangelo's David and not all of the art depicting slavery in Renaissance Italy, Raymond Chandler and not the dime store pulp.
It makes sense of course, because yesterday's slang is today's cipher and works that can stand the test of time must be at least recognizable to modern society. But it also gives a false impression of being truly representative of the era, when it's a narrow and often shrewdly calculated viewpoint that has been curated for you all these decades later.
And it's worked well here, as it's convinced you that the era was a time of high formality and bureaucratic industriousness.