Everyone just tells you, "oh now this can be a matrix." Nobody tells you why matrices are useful, or how we ended up with them. Just, you know matrices use them.
As anecdotal evidence, most math teachers I had in college were at best uninterested and at worst disdainful of applying the math to the real world beyond theorems in a blackboard. Most physics teachers, however, in introducing us to new concepts made an effort to show as soon as possible how the definitions we made were inspired by real world problems and in turn simplified or helped create new physics. This made it much easier to appreciate the pure math itself.
The response is often, No we do X because of Z. Which often you're learning Z. So now you just feel lost and confused. Its not 2 classes later until you'll learn A maps Y to Z and X is actually an operation of A so it applies to both.
I guess it's just me but the joy of math has always been its tangled relationships to itself.
You mentioned opengl and it's a perfect example of why you need to learn both. The Model matrix is column-oriented - if Z is up in the model but Y is up in the world, you need a Y unit vector in the third column of the matrix. The View matrix is row-oriented - each row is an axis of the camera's orientation. The columns perspective also makes it easier to understand homogeneous coordinates.
The article is right in my case, I didn't learn the intuitive understanding at first, and it could have been taught that way. It is also well written, for people that know math, but I also feel like the article describes math using more math, and that the point could be better made with a picture or two. There's something about just seeing the correspondence between matrix rows, or columns, and the axes of a space, or transform, that finally helped it all sink in for me.