It’s kind of a cause and effect thing that designers use. Of course, from calculus, you are right. But for instance in practice, you charge a capacitor with voltage as the outcome. You don’t look at the voltage, and then differentiate it to infer the current. Indeed, you get into trouble if you think you can put an independent voltage source across a capacitor. With an inductor, you build up the flux by applying a voltage. In both cases, the fundamental idea is the electric or magnetic field stored energy in the component, which the component acquires by accumulation, i.e. integration.
