Backpropagation is a leaky abstraction in the sense that every algorithm/physics-principle/mathematical-theorem is a leaky abstraction. Take 'sort.' If you use a sort API for large N in a performance-critical section of your code without knowing if the implementation of that sort is an insertion-sort or a quicksort, "you would be nervous." Hence you are dealing with a leaky abstraction, per this article.

I would much rather respond to the students who ask about why they need to know the details, by saying "because you registered for this class."

Essentially the question "if you’re never going to write backward passes once the class is over, why practice writing them?" is another way of asking "why reinvent the wheel?". And the best answer is "because learning is all about reinventing the wheel". The "code reuse as much as possible" mantra applies to when you're "using" a technique to do something else, not when you're "learning" the technique itself. They might as well register for Calculus and ask "why learn integrals and derivatives when mathematica can do them for you", or take an Aerodynamics class and ask "why learn fluid mechanics and dynamics, heck newton's laws, when an airplane can run on autopilot." I doubt "because calculus is a leaky abstraction" or "because fluid dynamics is a leaky abstraction" is a good answer to that.