The best analogy can be in the way we walk. Just think of it--we step on one leg and the weight of our entire body concentrates in that little footprint. Once we step on another leg that whole energy from the first one gets released, with the first leg being completely relaxed in that "standby mode" I mentioned earlier. When we walk it is so natural for us that we can say: "I am relaxed". All muscles work in tandem and our body does not collapse because of that constant muscles firing-relaxation and that natural re-distribution of energy.
I know that you're a fine pianist and I know that the analogy works for some. However, as someone who was actively harmed by thinking this way, I feel compelled to point out differences that must objectively be going on, unless the key is to be released immediately upon relaxing. All I ask is that you keep an open enough mind to read what I have to say and to consider it before replying.
The problem with your analogy is specifically that a key stays depressed. Even if we assume no arm weight is being applied at all, the springs of the key are trying to raise it back up. A relaxed finger cannot resist a spring. So what does, if you "relax"? Some people will claim arm weight does. Yet, equally, if any arm weight at all is involved, that too is trying to squash the hand into collapsing from the top down. Relaxation stops neither from causing movement in the hand and fingers. Only a proper use of specific ongoing activity (in the opposite direction to the springs and to the weight) stops significantly bigger tensions from achieving that necessary job. An accomplished pianist who thinks they are relaxed may be doing that balancing expansion activity without knowing. But an average amateur who is told to relax may be actively led away from it and towards the unconscious stiffness that must compensate, to stop the key rising. Ultimately, if you think you're fully relaxed in this situation, you aren't- whether you're a pro or a beginner. It falls to a pianist's skill and training to determine whether the actions that they keep balance with are effective ones, or messy tense ones.
The most common mistake of 99.9% students, which were not taught professionally, or were not taught well enough from the very beginning is the lack of that relaxation after the muscles firing. In other word, once the students push down the key they still keep it pressed at the bottom and the fingers "get stuck" in the keys--the louder they play the worse this feeling.
Why are they stuck at the bottom at all? If they get stuck, it's because they collapsed downwards. If they learn to push away, as in a press-up, there's nothing to let go of, except the balancing action. You finishing by being sprung AWAY from the keys- not by sagging down into them. The action that pushes you away is useful- not something to let go of. You fall down again if you release it. It's a matter of seeking BALANCE- not generic and imprecisely defined relaxation.
Consider what happens in a press up. Do you relax, at the top? No, because keeping some of that same activity is essential to staying in balance. You merely move to that point and then try to avoid being stiff. The more you open yourself away from the floor, the lighter the workload on the muscles. The worst thing is to relax towards the floor- which increases the level of effort required not to fall face first. Relaxation isn't beneficial. The best pianistic action just finishes into balance, like at the top of a press-up or after standing up out of a squat. There's nothing superfluous to relax, when it's done well. Even if you were tense somewhere, you cannot afford to strive for relaxation in all muscles, or you simply cause more tensions still. You need to feel which ones have an active role to maintain.
Consider/imagine throwing darts. Even if thrown with max speed once the dart pierces the board entire energy immediately disappears--there is no pressure, whatsoever, other than the dart staying stuck in the board.
The similar happens playing piano. Once your finger "pierces" the key entire energy should get immediately dissipated. Do you need pianissimo--your finger pierces it lightly. Do you need fortissimo--it pierces it with lot's of force (creating very fast hummer acceleration). But the feeling always should be the same--the piercing and immediate energy release is a simultaneous process.
This is exactly what harmed me the most. I'd succeed in letting it all go, as you describe. So I'd then relax and droop- which allows gravity to start tugging the knuckles down towards the keys. Then I'd instantly be forced to stiffen to stop my hand falling palm first into a cluster. I don't release anymore. I finish the equivalent of a press-up and exist in low-effort balance there, without letting anything even begin to fall back down again. The change in how little effort it now takes is too big to convey. Trying to relax (rather than get to know my balance point, by finishing the movement) caused my tensions.
The darts analogy just doesn't work, sorry. A dart has nothing to do. It's in balance anyway. A hand has action to perform if it is to retain balance. Some level of weight and springs in the key are trying to deform the shape. Only activity can keep balance. Relax into slack and be forced to hold up the weight of that slack through tension.
It's simply nothing like a situation where a dart could not fail to be balanced, and need do nothing more than exist. The more I tried to think that way, the more I relaxed the low effort actions that could have been balancing my hand simply and easily. And the more I unconsciously resorted to much greater compensatory efforts- as the only way to stop the key coming back up and my hand from falling down into a cluster. The analogy works fine in conjuction with superb teaching (that points at something else altogether), but in itself it points to all of the wrong things for anyone who wants to avoid wasted efforts.