You can replace chemistry with math in his article (and he sort of mentions this in context near the end). I can't remember once being shown the physical problems that drove progress in math until I reached calculus. I remember being bored to tears in algebra 2, a class which was basically being taught as linear algebra + trigonometry. It wasn't until the following summer that I discovered 3d transforms, and a bunch…
Boring is subjective. Many people find ”practical applications” boring but pure math fun. They would find your proposed curriculum deeply uninteresting.
The reverse is more difficult. My linear algebra teacher didn't ground the work in anything and as student I had no idea that the vectors and matrices could be used for, say, computer graphics.