The University of Florida has two separate math tracks: One for math majors and the other for engineers. As engineers, we really don't need the derivation, we don't need to see the inner beauty, we only need to be able to apply the results of the derivations. In fact, there is pretty much a slide away from even solving advanced equations by hand. At my grandson's university, MATLAB is used for everything. His Differential Equations course was more about problem solving with MATLAB than the underlying elegance of the derivations. Terrific! It's the application that's important!
I don't personally care a whit about how the equations and derivations came to be, I just want to use the tool. I don't need the history of fire, I just asked for a match.
This is fine if you are content to spend your life retreading old ground, but its not a suitable grounding for doing novel things. Matlab is a blessing for the working engineer, but its a curse for students. I lets them avoid understanding anything they do, and they are increasingly encouraged to take this path. If they have any aspirations it will come back to bite them.
For years, I had the same position, coppice.
Then, I realized that in math, unlike in most other fields, one does not need to "forget" things to learn a new approach, because the different approaches never contradict. In physics especially, we use approximations, and it is sometimes a hard knock to realize that stuff that you've been told is a hard law, is actually just a model that applies only in specific circumstances.
So, the cost of that "bite" in math is just taking the additional courses: additional study time. Worst case, the quick Matlab/Octave path was just wasted time.