Hey Lorrae,
I'm aware of the Golden Ratio, but this is still coming from fallacious thinking--you can try to apply pseudoscience and you'll certainly be able to come up with trends, as you've noted, but that is not a universal application and the idea is still extremely Western-centric, and the age of television is and always will be inextricably linked to Western white supremacist beauty norms.
Facial beauty absolutely is a social construct because beauty in itself as interpreted by a contemporary human lens will never be distinct from the social applications of attractiveness; the moment you were born, you were instilled constantly with a barrage of subliminal and open messages about what constitutes "beauty." It's quite impossible to show that based on an alleged likeness of this theory even from figures in ancient civilizations (many of which in reference to this study are interlinked through trade and shared media, including things like pottery and other artistic mediums--extra emphasis on media there because even ancient civilizations were subject to the same kind of mediation and acculturation of beauty that we are today) that that must mean there is something wholly "natural" about a homogenous form of beauty.
I know this isn't what you're getting at but this is the kind of pseudo-science that has absolutely been weaponized by Nazis and other eugenicists who believe in a certain concrete homogeneity of what is "beautiful." It will always be rooted in opinion, no matter how strongly you feel it, and no matter how much you see it reflected around you; there is a tendentious confirmation bias that happens when you are looking to reaffirm your perspective on what's "beautiful" in a concrete way-- sure, even if it does constitute the majority of people, you can never ignore the legions of people who are attracted to people who don't conform to those standards of beauty and you'll never fully account for the insecurity of the masses who seek vindication in something offered to them as "the right way" so they don't have to think for themselves or accept their deviations or the perceived deviations of people they are attracted to but don't want to admit it (see also: gay men who stay in the closet). Attraction is a finicky thing and there's no doubt that much of it is inborn, but there's also no doubt that much of it is socially constructed, including facial shapes.
You should be weary of numerical measures like this that attempt to quantify things that are objectively qualitative and cannot be reduced to numerical pseudomath; the BMI is another example of a numerical system that has been widely accepted despite its basis on very white supremacist, male-centric standards of what is "healthy," to the great harm of masses of people whose entire conceptualization of "health" rests in something that doesn't fully or in many cases even remotely speak to the actual state of their general health. I wrote an article about fat-shaming that goes into the details of this further that you are welcome to check out if you like.
I think it'd be interesting to lean into what it is that makes you desire a scientifically proven, universal conception of beauty so deeply-- and what makes the randomness or heterogeneity of "beauty" feel so impossible to you? Just a gander here, but in a capitalist society that constantly tells us how we're supposed to look and be in order to be "attractive enough," many of us are very used to making profound and painful sacrifices in order to meet these expectations (which none of us ever really do), and to knock down or challenge those standards could be like a tumbling house of cards. Incidentally, I do find it interesting that you allude to the abuse of societies trying to fatten up their women, when there are innumerable examples of how people get butt lifts, face lifts, lyposuction, endless other surgeries, rip out eyebrow hairs, wax off other body hairs, and even do things like wear high heels that physically restrain us and harm the ligaments and obstruct circulation in our feet just to appear as beautiful in this very repressed, sexist and racist society. Beauty for humans across time and space tends to be equated with sacrifice and subordination, because many of the power dynamics in sexual contexts (which inform the fundamental basis of "beauty" and attraction across the animal kingdom) involve some kind of differential. But the degree to which and the manifestation of those differentials are variable, and no attempt to perfectly calculate that will ever represent the spectrum of nature vs. nurture, nor the endless variability of expression and evolution that is part and parcel to life and existence.
Here's one article where you can read a bit about the limitations of the golden ratio theory:
