Power makes sense for steady state conditions. A certain energy will be used over one second. Then the same energy will be used the next second. And the next second. If I told you that such a circuit used 3 J, the first thing you'd ask is "When?", "Over what time?". Only knowing that is used 3 J at some time if it's doing the same thing over and over again is rather useless.
What matters in that case is the energy used per time. That comes up so often that we have a special name for it: "Power".
In some cases energy usage is "one off", and then it does make sense to talk about energy instead of power. For example, charging a capacitor to a particular voltage takes a fixed amount of energy, regardless of how fast or slow that energy is delivered. The same is true for how much energy an inductor can store before it saturates.
Power and energy are different metrics, so they have their different uses. We use whichever fits best to describe whatever phenomenon we are talking about.