I think a course like that would need to be called something like “Mathematics Appreciation,” in analogy to “Music Appreciation.” I would never hire someone whose only music education was the latter to actually play in a band or write a movie score, and I would never hire someone who didn’t know how to do differentiation or elementary integration by hand to do any work that required an understanding or use of calculus.

Now, there is such a thing as overkill in assigning calculus homework; integration problems can be made arbitrarily difficult, and past a certain point I don’t think there’s much educational payoff.

But learning advanced math is hard and requires hard work. Sorry about that. Math students often start off in elementary school finding everything easy and intuitive, but then at some point everyone hits the wall. Same thing can happen when learning a language or developing a physical skill. At that point there is no alternative to working hard in order to make progress past that wall.