The fact that there is a precise analogy between how Ax + s = b works when A is a matrix and the other quantities are vectors, and how this works when everything is scalars or what have you, is a fundamental insight which is useful to notationally encode. It's good to be able to readily reason that in either case, x = A^(-1) (b - s) if A is invertible, and so on.

It's good to be able to think and talk in terms of abstractions that do not force viewing analogous situations in very different terms. This is much of what math is about.