As someone who struggled with the "engineering calculus" track and switched to the "humanities calculus" track to do an economics major, I don't think the problem is with the material. I think it's a combination of poor teaching and overemphasis on computing results as if it were "fancy arithmetic" to be used daily.
It's worth being made aware of calc so that you can seek it out. It has applications aplenty. But that's a different role than the one it's presently in. For many calculus problems encountered in the real world, you can hand your data set over to the computer and get a numerical approximation back. For the ones that don't respond to that treatment, you can, most likely, look up tables of identities and find the ones you need to get the analytic solution.
There's some pedagogical idea that you can build your math intuition from working calculus problem sets, but that really isn't what happens in most classes. It's done by rote to keep continuity with high school math - the students because it's what they know, and the professors because it eases their lives. And so they struggle through a few semesters, and then some students go on to try advanced mathematics and encounter a completely different universe where math becomes proof-centric and they have to engage a different skillset that is more reminiscent of philosophical reasoning than anything they have probably encountered in prior math courses.
So it's a charade. You could spend much less time on any one field as a single topic, approaching higher math from an information-sciences perspective where you learn to seek out the forms of mathematics you need, engage in some inductive and deductive reasoning, and learn study techniques for math texts and papers(and hence, how to really gain insight on advanced math topics) to supplement your primary field - and not make any of it a bogeyman of higher education.