@Deadoks really good attempt and I'm sorry for condensing so much in those sentences. It is a characteristic of my job, most times.
Let's deconstruct what you said and I will explain the insight a little better, afterwards.
You see exercise as the trigger that activates the body's energy management system.
So, in your view fitness is a system employed to help us better manage the energy of the body.
The first part of what you said is not quite right but the second part is inspired and clearly you thought about it a lot!
Here's what I meant: The body will spend energy each day doing tasks regardless of whether we exercise or not. In a pre-industrialized world we would lift, walk, run, dig, etc all day and stop to fuel ourselves at lunchtime (maybe) and at night. We didn't need to exercise. In the modern world we don't have to do any of these things. The body gets way too much fuel (which it stores in fat in case it is needed) and gets to expand way too little energy. Exercise consists of additional, structured, physical activity which increases the body's energy output. It is only necessary now because we no longer lift, walk, run, dig, etc all day. So, structured exercise is the system we employ to better manage the energy that goes into the body and to help increase the energy output of the body so the two balance better.
The popular idea of fitness is a strong body (big muscles, six-pack, lean body etc). But the body itself doesn't actually care about any of this. These are things we strive for because of cultural norms regarding fitness. What the body will adapt for is doing something that feels hard (and costs a lot of energy) more easily. So it will increase strength, speed, endurance and so on so that it can reduce the amount of energy required to carry out a specific exercise. This fits in pretty well with the second sentence you wrote. Fitness (as I explained it) is indeed an adaptation that allows the body to do more with less (it's the reason why if we do the same thing all the time it stops helping us get fit). If we do get lean. strong, have abs etc that is just a by-product of the body's need to reduce the energetic cost of an exercise.
Thank you so much for adding your thinking here!