Warning, this post contains game theory stuff that might get a bit divorced from narrative storytelling.
The trick, to my mind, is to make the players think they won't win, because the enemies are too powerful or numerous. But then, due to the mechanics of the game, they pull ahead incrementally, because the PCs actually have more resources (HP) than they think they do.
That was the genius of healing surges. You see on your sheet that you have 40 HP, and so a monster that has 60 HP and does 20 damage in one hit feels horrifying. But you actually have 60 HP over the course of the fight, thanks to healing powers using your surges, so what looks like an impossible fight is actually fairly balanced.
The trouble, of course, is that 4e expected you to have a lot of "HUGE EPIC FIGHTS" every day, or at least the adventure writers designed modules that way. And people get fed up with having "HUGE EPIC FIGHTS" as random encounters.
I think hit dice actually work fine right now, since you only have a handful per day. I just want some way to use them without having to spend an action (standard action by 3e/PF/4e parlance). Or maybe magical in-combat healing just needs to be strong; I spend 1 action and you spend your hit dice, and we undo 2 or 3 actions worth of monsters-dealing-damage. We get ahead in the action economy by using up a different resource.