My unity edition hit point proposal:
Core
We'll assume some reasonable set of hit points, not too large, and balanced with the math.
You have two buckets that hit points can go in, "Hits" and "Points". By default, exactly half of your hit points go in each bucket. (If odd, put extra in "Points".)
"Points" are all the things that hit points have every been, except physical damage--but including narrative plot protection along with luck, fatigue, etc. The key point with respect to tradition is that except for being more worried (and thus perhaps more cautious), you fight just as well at 1 as you do at max.
"Hits" are pretty much "hit points as meat"--with perhaps a dollop of extreme fatigue/exhaustion, several pain effects, shock, etc. It's up to you where you draw the exact line, but there is no doubt that when you have damage here, you feel it.
In the core, the only direct, default difference is that if you are down any "Hits", you are "bloodied" and have a -2 to all attacks (but not defenses/saving throws, as we don't want too much of a death spiral by default). Alternately, this penalty might apply to skill checks. Alternately, there might be a handful of "bloodied" options that key on this state.
When you reach zero "Hits", you are dying. You must make a death save each round, or die. You can take no other actions.
With a short rest (as defined in 5E terms thus far), you can regain all "Points". In-combat restoration of "Points" is possible, though slightly biased against. Perhaps it is not proportional, and thus is used as a somewhat inefficient means of keeping characters up in a pinch. You can't restore "Hits" in combat at all, absent rare and limited magic. Out of combat depends on a host of variant options picked to fit the campaign (not listed here).
Common Variants (explained in the initial book)
"Hit Points as Meat--Hurts All the Time" - Everything goes in "Hits".
"Narrative is King, Baby" - Everything goes in "Points".
"I Played a Wound/Vitality System on TV" - "Hits" are equal to Con score. Remainder goes into "Points".
Common Options (also explained in the initial book)
"Not a Shread of Death Spiral" - No penalties for being out of hits, though you may still have some roughly balanced positive/negative effects from "bloodied" and/or longer term effects.
"Early D&D Hardcore" - Hit zero on the old "Hits" score, you die--no save, no muss, do not collect 200 dollars--you die.
"I Like Me Some Fiddly" - Various "wounding" options that key off of various things, such as each piece of damage to "Hits", crossing thresholds in same, etc.
"Changing the Dynamics" - Various options that change the pacing of play, such as critical hits bypassing "Points" and other such things.
Comments
The key piece of this is that you do most of your style changes by simply changing which of two buckets the "hit points" go into. Since the "hit point" totals are the same either way, it is easy to balance adventures around this. If you want to go 100% "Hits," then presumably you have arranged to deal with that. If you want to go 100% "Points," ditto. They can give some basic advice on what this might mean, for beginners, and move on. Meanwhile, anyone that wants one simple total, and no muss, is only having to deal with a divided HP line in monster/NPC entries (e.g. HP 30/31). I think it's a small price.
Depending upon which options you pick, there are, of course, sometimes more convenient ways to think about the HP, for tracking.
Moreover, the "options" that start to have more effect than this are not so baked in that you can't see what they do, or how they do it. So if you, for some strange reason, really like 35% "Hits" and 65% "Points", all you'll need for that is basic multiplication. If you want to have a "critical hit table" with gruesome results, you know what it affects. If you want your mindless constructs to be all "Hits" even though no one else is, you know how that works.
Also, if a 5E DDI tool has this kind of thing built in (two actual buckets), it's not much harder to give people some ways to customize that off of a single total. Now your monsters and characters are printed out consistently with whatever rules you have adopted. It's a bit more trouble if you assume one bucket.
Why not let magical healing be relegated to curing various disabilities? Poison, disease, blindness, etc. What is so great about Cure Light Wounds? Is it really so interesting that we need to keep it in the game? 
