I think in-combat healing should be an option, but it should be a safety net, to be pulled out during fights against particularly tough opponents (or after the PCs have been particularly unlucky), instead of as an assumed part of a regular fight.
This means that there should be a fairly significant cost to in-combat healing, either in terms of actions (it becomes your significant action for the round), frequency (it is usable only a limited number of times per day), money (for one-shot or charged healing items), etc.
Out of combat healing is a slightly different matter, though - the traditional approach of limited healing even out of combat creates strategic tension (how many hit points will I lose in this fight?) but not tactical tension (will I die during this fight?) until the PCs get low on hit points. The 4e approach is more likely to create tactical tension in a fight, but at the cost of the hit point yo-yo that some some people dislike (get hurt, get healed, repeat).
4e basically does so by limiting the total number of hit points you can bring to bear in any one fight, and then allowing you to replenish that total during a rest. I wonder whether an alternate approach might be able to achieve the same thing while allowing for the gradual hit point loss paradigm as an alternative to the healing paradigm.
Let's say that every character has a "pain threshold" which is equal to his Constitution score or one-quarter his full normal hit points, whichever is higher. In any fight, once the character has taken damage greater than or equal to his pain threshold, he is unconscious and unable to participate further in the fight (the Constitution score minimum is there to prevent low-level characters from going unconscious after a single hit). Characters recover from unconsciousness after a short rest.
So, instead of tactical tension from the chance of death, we have tactical tension from the chance of going unconscious. Not as intense, perhaps, but better (in terms of creating tactical tension) than the traditional approach in which a character remains conscious until he loses his last hit point. To add to the tension, we can also rule that unconscious characters are subject to coup de grace attacks which can cause death regardless of how many hit points he has remaining.
This approach does create a small amount of additional bookkeeping. However, in most cases, it is enough to note either the character's current hit points or pain threshold, whichever is higher, on a separate piece of scrap paper, and record all hit point damage taken over the course of the fight there. Adjustments to the character's actual hit points can be done after the fight.