FWIW, after reading this thread for a while, I just want to throw in that IMO just because HP is fully restored after a long rest doesn't mean necessarily that all the cuts, minor bruises, sore muscles, mental stress, etc. are gone. All it really means to me is that you are at 100% "fighting capacity", rested enough to go back into the fray effectively. That might even mean the PC has a bruised or fractured bone or something, but they are able to push through the current pain and do what they have to.
Also, since the abstract concept of HP also includes skill, luck, blessing of the gods, etc., I imagine what a PC's hp are can fluctuate. Maybe one time it is mostly luck, another day maybe more skill, or reflexes, or whatever. So, while the character might still have bumps and such, perhaps the hp is pretty much luck for that next attack? Most of the abstract aspects of HP have no visual sign as I see it, thus resting and recovering to full hp or "combat effectiveness" as I sometimes like to call it, doesn't have to defy what people can experience.
YMMV but that is how I think of it.