The major difference being that Gatorade and coffee/tea are fairly cheap, where a healing potion costs enough to feed a small village for a week. I mean, I get that you can make full use of abstraction to hide the causality and make it less weird if you've already made the decision to go with post-hoc narrative justification, but can you see how the alternative makes sense for people who start with an objective reality as a premise? Why it's more satisfying to some people for a magical potion to have an obvious magical effect, so that using it confers the same degree of certainty to both the player and the character, and why it's important that a thing be defined as it occurs rather than in retrospect?
If you don't mind another scenario, what would happen in the first situation you described if you didn't have a healing potion on hand? The player knows that the character has only a few hit points left, and the character knows that he's un-wounded but can't complete his customary ritual. Would the character then decide to not press the fight? Or would you decide, in retrospect, that this time those wounds are real injury and you can't go on because you might die?
On the 1st paragraph:
Even though it is no longer a part of my agenda for a high fantasy, mythic d&d campaign, I can certainly sympathize with folks who consider process simulation and displayed relevance for off screen/backdrop setting components as paramount to their TTRPG experience. I spent a generous portion of my gaming career with these same objectives of the same import.
That being said, that ship has long set sailed for me. There is far, far too much inconsistency with the coupling of d&d mechanics to implied setting physics (laws of CoM and CoE, flying trim characteristics, atmospheric friction and drag, waffling gravity) for me to attempt to try to fit that square peg in that round hole any longer. It is much simpler and more aesthetically pleasing to avert my eyes, rejigger my perceptions and expectations, and pursue a different agenda with systems that propose a different impetus. My GMing experience, and overall gaming experience, has improved dramatically since then.
But make no mistake, I am a veteran of the ins and outs of your preferences. I know what they are and why you possess them.
on the 2nd paragraph:
1) The anecdote in question doesn't include something such as a pathological behavior regime to quaff potions or some kind of dependency. If you have a potion, it works, 100 % of the time, to alleviate a variety of ailments, perceived or real, from failing morale to fatigue to minor soft tissue injury, etc.
2) The question requires controls such as system and genre (among others including group makeup and PC archetype). Let us assume 4e d&d and it's inherent gonzo/mythic fantasy, high action/adventure conceits and tropes. Under those pretenses, PCs have a robust assemblage (some more than other and scaling with level) of resources to call upon in response to escalation and desperation. What's more, the force multiplication and synergy of group play is considerable. As such , there is typically a thematic and mechanical answer to the situation within one of those depos; eg Second Wind or another 1st party HS-accessing ability, deployment of a stance or immediate action that bulwarks the PC, deployment of a game-changer by a teammate, an archetypal suite of contingencies or actions for such a situation (such as a Rogue using an at-will move + stealth effect or a Bladesinger calling upon one of his daily uses of Bladesong and Arcane Strike to become a nigh invulnerable angel of death for 2 rounds).
Actually, this example you gave kind of illustrates the problem. People did not drink Gatorade from the beginning of time; they drank water, even though if you're sweating a lot you do need electrolyte replacement. People did not intuitively know that they needed this; they just knew that they were thirsty.
It was intended as a stand-in for any behavioral regime/contingency that affects, real or perceived, the disposition of the user. "Looking good, feeling good, playing good", is a meme that has application, and legitimate utility, regardless of era. A mental framework is augmented or atrophied by all manner of intangible rituals, visceral feelings (highly applicable to this conversation!), and (borderline silly) buy-in into empirically provable nonsense. Further, confidence born of past success in a crucible of fire, being appropriately (over) armed for the task at hand, and belief that your true destiny will inevitably manifest is a fundamental difference-maker; both for the outlook of the participant and their will to act.