Blink....
There's nothing inherent in magical-or-long-term-healing that is more realistic than a quick recovery system.
Blink blink.
Blink blink blink.
If you assume that your human character corresponds to, at least somewhat, a RL human, then you (probably, lucky you if not) know from personal experience that injuries take a while to heal. You also know that people don't just keel over and die (except due to exceptional bad health/old age) w/o injury. Therefore a character who is in danger of dieing should take a while to fully recover w/o magic (if it is possible at all, good luck "recovering" from old age w/o magic. actually, good luck to us all *hopes*).
...
Quite simply - how?
In what ways did - let's say - 1e support sprained ankles, severed arms, and cracked ribs better than 4e does? IMHO, it doesn't. HPs are too flimsy a mechanic to hold everything you want to hang on them.
1e: sprained ankles, severed arms, cracked ribs are all injuries. They decrease your ability to fight (lost hp, worse in the case of severed arms), and take a while (days, minimum, forever w/o magic in the case of severed arms) to heal.
4e: Either sprained ankles and cracked ribs (and gaping chest wounds or slashed throats) do not affect your character at all (you can be at full hp/surges with them) OR your character heals all physical wounds, naturally, within 6 hours.
Neither edition requires narration. One of the two editions can support narration w/o assuming either that your character is able to regenerate or that his body can be hacked to bits w/o consequence.
If you want to model long-term injuries, you need a system to support long-term injuries. Arguably, 3e's ability score damage can handle a lot of this heavy lifting. Arguably, 4e's disease track mechanisms can do similar. Regardless, it's not an out-of-the-box assumption of the game that a certain number of HPs mean anything other than ... well that number of HPs.
I think the crucial problem here is that it's senseless to argue about what HP's are. I think it's a lot more useful to debate what HP's do.
-O
And previous editions have a system to support long-term injuries. It is called the hp mechanic w/natural healing. We can argue about the accuracy of the time-scale they imply. Please don't pretend that the system isn't there.