Thanks for linking to graphicallinearalgebra.net . I finally sat down and read it today, and (loveheart-emoji). This stuff looks more complicated than just writing a bunch of matrices, but it really does go to the deep of linear algebra.
It is certainly more complicated in the beginning, partly because it is a paradigm shift, and partly because of the abstract nature. But then again, linear algebra isn't particularly natural when you see it the first time, I'd say..
But graphical linear algebra gives other powerful insights, such as the meaning of division by zero. btw. we use a very similar calculus