The theorems they prove in mathematician's calculus are useless for engineers, and they take time away from learning useful tricks for doing integrals, which if not that critical for a world with numerical methods, are crucial for solving problems on future tests.
> The specific theorems students prove are not really the point.
Right, that's why they should skip the calculus and start students directly on Real analysis. Then they might actually have some use for what they prove in the class.
I prefer to know where the formulas come from, to know when the formulas apply, when they don't apply, what their limits are, and how to adapt them to a specific problem.