IMHO the absurd market value and crafting time/resources were likely chosen because -despite having item rarities- rarities aren't handled well in this game, especially at higher levels of play. Everyone expects that a "common" potion of healing should be available in unlimited quantities, so if the price is low, any sensible character would wear a bandoleer of healing potions at all times. This conflicts with the ambiance the designers wanted, so they jacked the prices up. Add it to the list of ways the designers ham-handedly attempted to maintain a medieval economy in a world with magic that gets described as rare but presented as common.
I think potions requiring a short or long rest would have actually fit the medieval fantasy tropes a lot better anyway. I like the idea of a healing potion that automatically stabilizes the creature and then restores x HP after some period of time. More rare potions could grant x HP immediately and y HP after a rest or something.
Yes, agreed (first paragraph) and I like your idea (second paragraph).
I think part of the "problem" (such as it is) is that the D&D world is generally envisioned as a quasi-medieval world with magic stuff
in it, not how the ancients and indigenous people of our world viewed (or view) our world: that it is ensouled, embued with lifeforce. Meaning, magic is intrinsic to the world and, in a way, it "grows out of it."
So a ranger or druid could theoretically know herbs or springs of water that have healing properties beyond just the typical skill usage of Medicine. In fact, as I write this I think I'd allow for a druid or ranger to make a Nature check on a short rest. Other classes with proficiency in Nature could still make the check but might be at Disadvantage (or maybe they aren't, and druids at least get Advantage). Something like:
1-10 Nothing found
11-15 herbs that offer d4 worth of healing
16-17 herbs that offer 2d4 worth of healing
18-19 herbs that offer 3d4 worth of healing
20+ special - an herb or plant (possibly mushroom) with special healing properties
Or something like that.
There would be a modifier, plus or minus, depending upon the environment. A desert might be -5, while a primeval forest brimming with magic might be +5.