I can, even 10 years later, not because I'm gifted but because I had good calc teachers who consistently covered and circled back on those points. I know what you mean though.
But what I mean is that 25th time you're doing an integral to ram home some trigonometric identity or working out a fourier series for PDEs it's not because anybody hopes that this is the time you get the epiphany it's because the teachers need something for the grade books and you need to be able to do it during a midterm.
Assuming Wolfram wasn't engaged in just an attempt to sell more mathematica licenses I would assume that was kind of his point. If you dump the most of the endless repetition on to maxima/maple/mathematica you could actually spend the semester on the concepts and proving them instead of focusing so heavily on the student's facility at algebraic manipulation.
Now having had to do everything by hand I have the sort of knee jerk reaction that "well I had to do it so they should do it too" but then I also remember that it sucked giant balls. As I see it is students definitely need pretty solid facility at doing this sort of shit and so we get the classic: "where do we draw the line" problem, which means I should probably not be counted as a proponent of Wolfram, so much as maybe a sympathizer (in this regard; fuck NKS).
*also while I take didn't real, I did get a minor in math which included Basic Concepts of Mathematics, or as I tend to remember it "that semester of not being able to divide because it's not defined over the integer set" but it was certainly a purely proof oriented course, and my numerical methods 1&2 were at least 50% proof based, I've done the formal rigor thing.
To this day I remember how outraged I was that on my final for Calculus 101 I derived from scratch an answer to an integration problem, then did the derivative and proved it was right on the final exam. Then the grader, upon seeing an answer different from the expected one marked it wrong.
I understand the grader was in a hurry, and the trig identity demonstrating that my answer was, in fact, equivalent to the standard one is not easy. But I had the right answer! And proved it was right, right there on the test!
I still remember the outrage. Over a question that did not matter then (I got an A+ in the course either way) or now.