No, it isn't. This is another dumb platitude spouted by the crowd that really needs to vanish.
"Beauty" is based on geometric and biological axioms
https://www.goldennumber.net/beauty/
Cultures everywhere in the world have beauty standards that conform to the Marquardt Beauty Mask and the Golden Ratio for facial beauty. This "beauty is in the eye of the beholder" meme needs to die. There may be MINOR differences in "tastes" from person to person, but these are more based on sxxual fetishes (some men like asiatic monolid eyes, some don't; some like lighter skinned women, some like darker; etc) than they are on aesthetic sensibility. Ugly is ugly, beauty is beauty, regardless of the "beholder".
Okay, I wanted to get back into this discussion. I don't think beauty is fully objective (even your post alludes to it), but let's leave that aside for now. Your evidence points facial beauty is mostly objective.
We were talking about insurance / healthcare here. No matter if all scientists in the world unanimously agree that beauty is completely objective at some point in the future, no insurance or healthcare system is going to cover cosmetic surgery for people who don't score near a Golden Ratio facially. The reasons are obvious. It'd sound offensive to the vast majority of society, it'd be bad PR, and not politically correct. Adding to that, even if facial beauty is completely objective, it is actually malleable, unlike height. Every man can look facially better by working out to the point they get a lean face. Change to hairstyles that make their facial proportions look better (and become more attractive in the process). There's a lot of reasons why it would never be covered by insurance or public healthcare even if unanimously agreed on by the scientific world. I know this is not the point you're arguing, but I wanted to get into it.
Onto height: there's nothing that can be non-superficially done about height (at least in the mind of current society). It is also, sadly, a major physical feature for sexual attraction. This means it is incredibly hard for women at heights like 190cm and up, and even worse for men at 160cm and under. Unlike beauty, we can easily say someone is "tall" or "short" without much fuss. Once a safe technology and decades of psychological research are there, it'll be much less of a problem for insurance and healthcare systems to cover people on extreme enough height percentiles. It's a quick and objective measurement. Adding to that, heightism even helps there. There's very few, if any, organizations promoting that extremely short men are just as beautiful as average height males, and that they should embrace it. It's just not a movement.
We already have history with insurances and some healthcare systems covering sex-reassignment therapy and surgery, HGH treatment for HGH-deficient children, etc. It's not a stretch to think that men in extreme height percentiles will be able to get height surgery in the distant enough future through health insurance or public healthcare. I think it'd be harder for women, but I'd hope extreme height percentiles in both biological sexes are treated equally, should people want to get treatment. This is all unimaginable for the treatment of "ugliness". No matter how "objectively ugly" someone is, it'd be disastrous PR for any insurance or healthcare system to cover cosmetic surgery for it. The best comparison that could be made, and still an unfortunate one, is to burn and acid attack victims. Their facial and other plastic surgeries would/should be covered by insurance and public healthcare systems.