It's useful for solving (or partially solving for a set of conditions) linear differential equations, say in the fields of mechanics or electromagnetism. One can work with dx and dt as if they were just factors and move them around quite intuitively.

In the same line, it's great at shining a light on the substitution rule for integration.

Given that your point that it can be obscure at first remains valid, I'd walk the middle line of introducing students to the f'(x) notation first; and after the introduction to integrals introduce this notation to them.