Long-term wound healing is boring and tedious, which is why they removed it in 4e, I imagine. You lose the narrative of lying in bed for 6 weeks (wow, can't wait to roleplay that!) in exchange for gaining the narrative of taking a sucking chest wound at 4 in the afternoon and still being able to rescue the princess by midnight, when her soul would be sucked out by the evil sorcerer using a diabolic ritual. With long-term wound healing, your only choice is to ransom the dried husk of a corpse so her family can bury it properly. Oh, but there's always magic, magic trumps everything, which is a major failure of 3e, IMO. But that's another thread.
Well, I like the narrative options of:
(1) Taking the chest wound and dying. End of story for this character, but potentially very interesting to the other PCs, or your new character. This narrative might send your party into a revenge-driven rage, it might make them rethink every decision they made that led up to this, it might make them more cautious, or it might make them more reckless. The narratives are varied and interesting.
(2) Taking the chest wound and having to spend days or a couple weeks recovering (if you have no way to heal near you). This lets the setting evolve, and opens up narratives you wouldn't see if not for time spent recovering. For example, the princess dying might be a very interesting narrative to explore, since I assume she was killed for a reason. Non-death failures are very interesting much of the time.
(3) Taking the chest wound and not even slowing down. That is, it's not very much HP damage, and you push past it, or recover it overnight. This, too, opens up the narrative of being wounded but continuing to save the princess, which can open up some really interesting narratives that aren't able to be explored without this option.
I think there's a lot of interesting stories to be told in a system that allows all three. Number (2), however, is something I don't want to go without. I love things that give the setting time to evolve. That is, I don't like long distance teleports or plane shifting being a common option for the PCs or the setting (something 3.X failed hard at).
Having to hoof it everywhere gives the setting time to change naturally, which can really propel story forward. My 3.X game only got hard to run once transportation magic became common to the PCs and the setting (the setting couldn't use magic for a while for story reasons). It was hard for anything to build up without it getting beaten down before really getting off the ground (divination was another huge culprit here, and it really failed me in 3.X as well).
At any rate, it's not the "you're bedridden for a week!" that's interesting, which is why it usually gets skimmed over pretty quickly. It's what happens with the setting in that time that's really interesting. And that's why I want long term wounds in my game. But, as always, play what you like
Most players I know don't like long periods where they're out of the action, or losing characters. There are a few hard-core roleplayers that get into that kind of thing, and some that don't get attached to their characters too much. But most players want to be kicking ass and taking names, not dying or nursing wounds for any length of time. 
