While I am very happy with 4E's "two dimensional" healing, where a character's resistance to death comprises both "width" (hit points) and "depth" (healing surges), I do view this as just one possibility for a functional and enjoyable roleplaying game.
To be "functional", though, an RPG should be consistent in its general approaches to magical and "mundane" happenings. It's possible to be "subtle/realistic" or "gonzo" for either magical or mundane effects (including healing). 4E goes "gonzo" for both; hit points are used as a dramatic "reserve" of plot immunity, in effect (although you can imagine that effect in a myriad different ways, to suit your tastes) and as such recovery by "Second Wind" or between fights and by "leadership qualities" make perfect sense to me.
Systems that use subtle/"realistic" magic and "realistic" non-magical effects also work really well, for me. Systems that don't use hit points or classes and levels work best, here, I think, but some flexibility is possible. HârnMaster is the poster child, but RuneQuest, GURPS and Shadowrun can scrape in here, too.
What I find works poorly, for me, is mixing subtle/realistic "mundane" with gonzo magic. That just leads to a "Wizards (including variants like Clerics, Druids, etc.) Rule the World" trope that I find tiresome unless done well (as in Ars Magica, for example). I would probably say that subtle/"realistic" magic and gonzo "mundane" stuff would suit me poorly, too, but oddly enough no-one seems to have made a game with that approach...
Mid-period D&D - peaking with 3.x, I suppose - I found to push furthest towards the "subdued mundane/gonzo magic" model, which is why I responded so enthusiastically to 4E (along with the fact that the rules are straightfoward enough for me to actually know how they work, as opposed to simply memorising a whole mass of detail).
For DDN? Well, I hope it keeps the "level of gonzo" even between magic and non-magic - whatever general level it selects - and that it keeps a core rule engine that is easily comprehended in its entirety without memorising all the powers (spells and class features).
Healing fits into this overall picture in that I want the "mundane" and magical healing to be either both gonzo or both subtle/"realistic". Having magical healing work instantaneously and "mundane" healing work glacially slowly does not fulfill my wishes at all. On top of that, game considerations must be considered. Healing that is not limited by any important resource - whether it be "Wands of CLW", "Healing Potions" or "Healing Herbs" that cure 1d3 hp for 1gp a pop - makes a travesty of supposed in-game danger (which needs to be limited, but not non-existant).
So, in summary - I'll take both "magic" and "mundane" healing that has distinct game limits (i.e. uses character resources or exposes users to independent risk) and where both types are in balance regarding "gonzo-ness". Fluff it as you wish: healing herbs, poultices, laying on hands, flash miracles from a wand, "shouting back alive" - whatever. Ideally, just give a taste of the game-world process involved and let the players imagine it as suits their own imagination; trigger the imagination, don't try to force it into a specific mould.
Does that answer your question?