Healing

 Potions of healing are properly Potions of Magical Healing.

Natural healing in D&D is accomplished at the rate of 1 HP per day. Binding a wound or setting a broken bone does not have the same effect upon a character as magical healing.

The effect of a potion is identical to a spell of Cure Wounds. Cure Wounds does not cure disease, remove poisons, unclog arteries, or reverse aging. If every spell was free and every priest knew Cure Wounds, that would still not stop death from natural causes. (There are spells to reverse those other debilitating conditions, though).

A wealthy person with high level priest spells on tap could conceivably prolong his life through magical means. This happens today in the real world with people who live on life support. In the real world, some life support procedures are especially painful, and are not guaranteed to work. D&D magic is always reliable and not especially painful, so the real cost of using magic is the Vancian casting system. Magical healing in the D&D world might prolong the life of a character and improve its quality beyond what it was for actual medieval citizenry, but the high cost and low availability is the only reason it’s not available to everyone all the time. Even the highest level Patriarch cannot heal, cure, and reverse the aging of every infirm person in the city.  That service is reserved for the privileged.