Most colleges I'm aware of these days have a completely softball core math/science requirement. "Rocks for jocks" and that kind of thing. Whether it's a waste of time or not, I don't think it really impedes the serious math learners.
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.
"Whether it's a waste of time or not, I don't think it really impedes the serious math learners."
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"
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.