In truth, middle-mathematics (undergrad university courses, henceforth lumped into the "calculus" umbrella) is a proxy for symbolic reasoning. The grungy part is looking at an arbitrary problem from your area of expertise, realizing that it's fundamentally a calculus problem, and then rephrasing it as a calculus problem and reinterpeting the solution back to your area of expertise. People have a hard time doing that if they aren't familiar with the actual nuts and bolts of calculus -- in my experience, every student that comes out of a "black box" course is entirely dependent on the specific tooling they were exposed to and typically has zero curiosity about what lies beneath -- those students tend to not get very far.

Likewise, we still teach bubble sort because it's an easy thing to teach rudimentary proof skills with. Similarly, we start students off with Newtonian physics.