I like your spin on it. Can you elaborate on your ideas? I wish I could make it more interesting for my students.
We had to go through about a month of "mechanical" learning of differentiation just to get them over the rules. Walk before running and what not.
When we got to the problem solving stuff, they'd forgotten mostly about the techniques, or they were learning how to do the problem by copying / referring to a previous problem of the same style.
Of course, one could argue we could dispense with all the techniques of differentiation / integration and just focus on its applications in the real world, using something like WolframAlpha to do all the mechanical calculus for us.