But here's a point I would have liked examined further in the article: where does one find material or instruction that would give you a competitive structural thinking needed to grapple Olympiad or Putnam-level content beyond enrichment courses? In China, the best students are scouted early by teachers and prepared by the Chinese government through special camps and their own difficult examinations. I'd assume the same thing happened/happens in Russia. In the United States, by default (and probably by design), its difficult to know on what level a student can stand in regards to everyone else until the very end. At least in a public school.
Parents and students can use proxies like how early AP subjects are offered, USA today rankings, or the success of past alumni. But, unless you're in a well-endowed private schools, magnet/exam schools, or private enrichment program like AoPS (Art of Problem solving) or Talent Identification Programs (many of which are now shutting down) there are few ways to know how well the instruction one receives as a precocious and motivated high school compare to those of the best among the nation or the world.
One could argue if you have to wait until high school to understand where you stand, it's too late. But that's my point, many students may have resources and talent but the lack the expertise to deciding where to and how begin in those crucial first years. Few states have strong "gifted" programs and the one's that do aren't really any better than "normal" instruction in China or Japan.
But even the non-Perelmans - the "regular" students - who didn't rise to the peaks of intellectual rigor still have a stronger background in today's knowledge economy then most of their contemporaries stateside.
As far as their children are concerned, the Russians and Chinese send their best 18 year-olds to Ivies, Ivy-likes, and Oxbridge just as they send their best 18 year-olds to Moscow State and Peking. Many of them prefer an American degree for the business opportunities, better income, and the prestige of working for an American firm. A more relevant question to ask is how many would send their best 14 year-olds to the average public high school in the US, or the average comprehensive school in the UK, as full-time students for at least 3 years?
By high school one can start seeking out their own resources, but motivation to do math specifically is harder to find when you've considered it a boring subject for 5+ years. And there is definitely an advantage to being introduced certain concepts at an elementary school age.
So the US approach absolutely differs in how it handles early math education for the vast majority of students, not just for the average student. I wish I learned math in the Russian style as a child, and moreover I think US math has this problem moreso than even other subjects here. Humanities classes generally have less mindless repetition and early childhood teachers could easily recommend advanced books in a way they really couldn't for math.
In many schools the same teacher will teach every subject until you hit middle school! So it is no surprise they don't have resources to give to advanced students, as a lot of them dread math themselves.
In the last 10 years nearly every school has adopted the Common Core curriculum, which is the product of the latest findings in educational methodology research, developed by Ed.D. luminaries like Dr. Jill Biden, and promoted by successful industrialists like Bill Gates.