And for understanding a normal school curriculum, it's much more important to understand derivatives than it is to understand the deep connections between constructive geometry and algebra, which is the kind of thing where category theory shines.

Basically, category theory in education proponents seem to forget that math is not just learned for its own self, but that it is also an important basis for understanding physics and perhaps other subjects.

Students also tend to do horribly with abstraction, it's one of the hardest things for some to understand. I've literally seen (very young) students who can tell you how many apples they have if the multiply 5 apples by 3 apples, but can't tell you how much is 5 * 3. Or who can tell you what's the missing number in 5 + _ = 9, but can't tell you what is x in 5 + x = 9. This may or may not apply at other levels of abstraction for older students as well.