Which country do you mean? As far as I'm aware, it's the opposite: countries like China and South Korea have math as a required subject on their college entrance exams for all students. The non-STEM students may have fewer requirements, but I'm fairly sure they've still learned more than the average American high school student.
https://en.wikipedia.org/wiki/Gaokao#Reform_of_the_National_...
https://en.wikipedia.org/wiki/College_Scholastic_Ability_Tes...
https://medium.com/@yujia_jo/2016-jiangsu-gaokao-national-hi...
I do know there are countries which allow specialization at the high school level (India, Italy, Romania I believe).
I found this interesting list, which is more complete than I can be on this. I don't think it proves that countries with great mathematical cultures always allow specialization in high school, but it does have some examples of this.
https://en.wikipedia.org/wiki/List_of_secondary_education_sy...
I think you are right that we need more flexibility on the high school level though, at least for juniors/seniors that have safely passed the earlier requirements. I like that we have a chance to dabble in various subjects in college here before committing to something, but it would be a lot more efficient if some of that could be done in late high school.
I thought about this for a bit. Suppose we kept the number of teachers (or courses) fixed, but eliminated the gen-ed math requirement. You would end up with a better teacher : student ratio, and I believe this would benefit the serious math learners. And so by not doing this, I believe we may be implicitly impeding them.
My guess is there are lots of ways wasted resources (and I do believe any class which could be perceived as "rocks for jocks"-type is wasted resources, and may actually be a damaging use of resources - I say this as a TA for the pre-major courses*, where the students are constantly and overwhelmingly negative about the whole thing) are implicitly impeding the serious students.
(And, as a positive note, I think the students not characterized as "serious students" for the above discussion could have a chance at meaningful and valuable contribution elsewhere, if we weren't putting so much effort into wasting their time.)
Edit: Changed "lower level courses" to "pre-major courses"