Yes, matrices got everywhere in the 20th century. There is basically no field that doesn't use them nowadays.
But any demonstration requires modern knowledge, and matrices are one of the very few modern thing students see. If you want to show them 3D graphics, you will need to teach programing first. Yeah, some will know it by them, but schools also can't rely on that.
(As an aside, chemistry also has some weirdly modern knowledge on its curriculum. Also out of context, just thrown in there because it's important.)
The nearest application I can think of is for modeling stochastic processes, but students see so little statistics that I imagine that will only change the object on the "why am I even studying X?" complaint.