Way too often intuition (or trying to make things clear on an intuitive level) interferes with and/or severely impedes and slows down gaining the actually useful skills. Maybe not in applications to computer grahics, but in genreral there is so much to matrix analysis [1] that trying to translate everything into geometric images would make learning it at a practically useful level anything but impossible.
Rote learning, like the mindless memorizing of the multiplication table, is an extremely important component of education that is to reach any degree of sophistication or usefulness.
Also, being not (too firmly) attached to a particular interpretation of a formal system leaves open the door to potentially discovering new applications.
I just love how a few posts over here massively upvote clearly simple comments such as "I had used a matrix in 3D and then used them to rotate points in 3D space" against somebody who may not clearly understand, yet still makes a point that matrices are way more abstract than people expect them to be - and they downvote because it's harder to understand.
This is such a horrible form of childish anti-intellectualism.
Rote learning, like the mindless memorizing of the multiplication table, is an extremely important component of education that is to reach any degree of sophistication or usefulness.
Also, being not (too firmly) attached to a particular interpretation of a formal system leaves open the door to potentially discovering new applications.
[1] See, for example, a book by Horn and Johnson.