These programs exist, but are generally separated from the ordinary high school system. For example, right here in the Bay area there's Proof School, a private school founded precisely "for kids who love math", AoPS Academy, for extracurricular challenging math classes, and powerhouse public schools like Lynbrook, where gigantic student-run clubs aimed at competitions provide exactly this kind of education.
Comparing the Bay to the American education system as a whole is unfair. In the more rural part of California I grew up we had no options available to us at all. There was the high school, and the more trade-focused high school that only existed as somewhere to put kids who had been expelled from the normal high school.
People do that with Soviet system too. In the 1980s, a disproportionate number of top scientific cadre were born and raised in Moscow and went through the few focused schools there.
Born gifted in Govneevka, Kirov obl., pop. 20,000? Good luck.
The system was absolutely flawed, still is, but still good enough to encourage the highly skilled.
Our (Romania's) education system was (is) the same, if you were GOOD at something there were plenty of paths that teachers would generally push you towards, special clubs for maths, languages, art (less common). Or schools who would try to group together highly skilled students.
System (after communism) has the same flaw, most rural areas have worse access to education, or better said, much worse quality of education.
