This is a topic I've thought about a lot. Let's forget about the pure/applied divide. That's not what I am getting at and I want to make my language very clear

This is a topic I've thought about a lot. Let's forget about the pure/applied divide. That's not what I am getting at and I want to make my language very clear. Let's instead talk about "maths for its own sake" and "maths for x" (physics, computer science, what have you). Calculus is a nasty kind of maths to study for its own sake. It's not intuitive, and it's shaped by motivations that aren't at all clear until you've learned its applications. Stuff like abstract algebra or graph theory on the other hand are - to me - "quite nice". They're certainly much more intuitive than anything in calculus world. So, basically I agree with you - in high school, maths (by which we really mean geometry and calculus) should be hand in hand with physics. I mean that is its reason for being in the curriculum, to prepare future engineers. People who want to study "real maths" can learn something easier to grasp, and maybe a bit more profound.