Okay, here’s the reveal (!):
First, people find a certain type of escapist pleasure in each of the three (Downton Abbey, Frozen, and Imitation of Life), and that is the pleasure of identifying with characters who have plenty of resources, beautiful living spaces, and lovely possessions. Downton Abbey and Imitation of Life are particularly full of gorgeous clothes, jewels, spacious mansions, etc. But even Frozen, with its 'cartoon characters have only one (or a couple of) iconic outfits’ convention, spends a fair bit of time letting us tour through the palatial halls and portrait-hung galleries of the gigantic castle that the princesses grow up in. (And of course there’s Elsa’s ice palace!)
So there’s that. It’s the same impulse-to-identify that made hits of reality-television shows that showcase the home of the wealthy and celebrated (with the iconic “Lifestyles of the Rich and Famous” making the theme as blatant as can be). 'Imagine what it would be like to have…’ is, without doubt, a popular fantasy.
Second, these three works have in common a philosophy that might be described as an implicit belief in the benevolence of those at the top. The basic idea: ‘Increasing wealth inequality is nothing to worry about, because those at the top are Kind, Warm, and Nurturing–all they want is to be allowed to take care of us!’
I’m identifying two genres, here:
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There are works of entertainment that vilify those at the top of the power hierarchy and assert the nobility and purity of those at the bottom. Many of these are more about adolescent psychology than about real-world power-politics (The Hunger Games, Divergent, etc. etc.). But this is an undeniably durable genre. Audiences never tire of seeing rich, thieving old Mr. Potter get his comeuppance when the common people of Bedford Falls rally to help virtuous George Bailey. (And so on.)
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Then there is the genre of works that is, basically, the opposite of the populist “rich people as villains” stories. These tell us that those at the top deserve to be at the top*, and it’s really okay, because they are such wonderful people! All they want to do is make us ice rinks to skate on! And it’s a happy, easy life to be a servant to them–you have tons of time to sit around and gossip; you have spacious quarters, the chance to fall in love and marry, and of course the assurance that no matter what, the Lord and Lady will take care of you if you become too sick or too old to work. (All of that latter is a prominent feature of Downton Abbey; none of it was actually true, for 99.999% of British servants.)
Both genres distort reality. The ‘people at the top are selfish, evil tyrants’ theme is no more reliably or universally true than is the ‘people at the top are altruists, who want nothing more than to tenderly care for those at the bottom’ theme.
*Possibly the purest expression of the ‘those at the top deserve to be at the top’ philosophy is the sub-genre of “switched at birth” stories. The child born of Noble parents will turn out to be, well, quite noble–despite being raised in poverty. And the child born of the underclass will turn out to be shifty or substandard or sickly (as in the recent SDMB Book Club selection The Woman in White).
A modern treatment of this “nature versus nurture” theme that subverts the ‘birth will tell’ (nature over nurture) philosophy was the 1983 movie Trading Places, in which the underclass in question was racial as well as economic. (The subversion was that both the upperclass-born and underclass-born characters turned out to be smart, capable, and sympathetic.)
A complex treatment of underclass/upperclass-born babies being switched was offered by Mark Twain in his controversial novel Pudd’nhead Wilson. Twain, sadly, did ultimately come down on the side of ‘birth will tell’ in creating the ‘switched’ characters. (And this post has gotten too long to go on adding examples.)