It’s cultural, at the very least. IANADentist/Parent, but I can tell you that any given American child likely has several friends with braces. It’s just seen as a part of growing up for a lot of kids. I wouldn’t go assigning malice. Pretty teeth are important to Americans, just like soccer is important to Britons but most Americans can’t figure it out.
Nobody said it’s a sacred cow. You’ve been relentlessly attacking an aspect of English life which the English have to defend constantly against Americans. I can’t blame them for getting irritated.
Recently my dad had a visiting Englishman over for dinner. The guy lives in Canada now, and my dad has always been a small-government type, so the guy fielded plenty of questions about Canadian and English healthcare. His analysis was basically, “It works for its purpose. People die waiting for kidney transplants, but then, that happens here too. The difference is that your position in line is based on how badly you need something, not how much you’re willing to pay for it.” When my mom came home a little later, my dad told her that they had been discussing “socialized medicine” and come to the conclusion that “it doesn’t work”, and the poor Brit had to explain it all over again. I imagine this happens a lot between Americans and Britons.