It’s just an arbitrary convention based on historical inertia. My impression/speculation is that prefixing functions comes from the historical process turning

It’s just an arbitrary convention based on historical inertia. My impression/speculation is that prefixing functions comes from the historical process turning prose into notation. You start with “sine of a” and that eventually becomes “sin a”, etc. Later the idea of a generic f(x) was from the early 18th century. The spatial organization of written matrix notation is directly lifted from the way people wrote systems of simultaneous linear equations. Just take the variables out and put all of the numbers in a grid.