Having just looked it up this is almost mechanically identical to healing surges. With hit dice mapping to the healing surge numbers. Given that a cure light or a potion is healing 25% of a characters max HP (same as healing surge) there is really no reason to also scale the healing dice by class. Since the 25% value will swamp the die result....
Anyway, all this long preamble is just to give context for a relatively simple idea I've been mulling over- making potions and cure spells proportionate to HD and HP in old school games.
The current idea I'm toying with is that the base value of a Cure Light or Potion of Healing, instead of being d6+1 in B/X or OSE, would be a d8 base for a Fighter or Dwarf, a d4 for an MU or Thief, and a d6 for everyone else. The plus value would be 1/4 of the character's max HP, rounding down. Cure Serious would instead do two dice plus 50% of the character's max HP.
One other benefit that just occurred to me would be that in slot-based encumbrance systems, healing potions also retain proportionate value for the slots they take up.
Whatcha think?
*(I get that Con does factor in, in some editions, like 3E and 5E)
The big difference is that tying them to Hit Dice is going to do weird things to the ability to last through encounters.
In 4e the number of healing surges was fixed by class (values ranging from 6 to 10) plus Con mod.
Low level characters will really want to go home and have a lie down after a single encounter and high level characters will be like energiser bunnies, depending on the HD recovery mechanics.