I'm a numbers guy, and looking at the numbers, I think that we can have the simplicity of tracking one hp total (no need for a VP/WP split) and have non-magical restoration of hit points in the same system, with the following assumptions:
1. Hit points are composed of physical hit points and intangible hit points (vigor, morale, luck, divine favor, etc.).
2. Physical hit points can only be recovered through magic or time. Intangible hit points can be recovered quickly, through a short rest, being inspired by a warlord, etc.
3. A 1st-level character has only physical hit points (based on Constitution). From 2nd level onward, a character's increases in hit points are solely due to intangible factors.
4. When a character loses hit points, he loses physical and intangible hit points roughly in proportion to his current physical and intangible hit point values, with a bias in favor of losing intangible hit points. For example, if a character has 10 physical hit points and 20 intangible hit points, and he loses 9 hp, he loses 3 physical hp and 6 intangible hp. If he loses 11 hp instead, he loses 3 physical hp and 8 intangible hp.
Now, assuming a typical character has a Constitution of 12 and gains 5 hit points per level after 1st, a character's intangible hit points would have overtaken his physical hit points around level 4 (12 physical, 15 intangible). So, a 4th-level character who has been reduced to less than half his hit points ("bloodied" in 4e) would have lost at least half his intangible hit points, and since his intangible hit points are more than half his total hit points, the intangible hit points lost would be more than one-quarter his total hit points. This means that when a 4th-level character has lost half his total hit points, we can restore one-quarter of his total hit points and quite safely attribute it entirely to the recovery of intangible hit points.
After we have done so, the character now has proportionately more intangible hit points and so will lose proportionately more intangible hit points each time he loses hit points. The next time he drops to half his total normal hit points, we can again restore one-quarter of his total hit points and quite safely attribute it to the recovery of intangible hit points.
This allows you to set the following relatively simple rule:
At 4th level, a character who is below half his total normal hit points may take a short rest to recover one-quarter his total normal hit points. In combat, he may do the same by spending a standard action to take a second wind (and a warlord or other non-magical "healer" may allow a character to take a second wind without the need to spend any actions). He may do so a total of X times per day (where X is some number which may be dependent on class or Constitution, or may be set by the DM depending on his preferred game style).
Under this system, an extended rest (or a day's rest) restores 1 hit point (assumed to be physical) and resets the number of times the character can take short rests and second wind actions. This means that while the character is on an adventure, he will normally be operating between 50% and 75% of his full normal hit points without magical healing. He can only recover all his hit points (non-magically) by taking a full rest, which is defined as a week (or more, at the DM's preference) of rest (no strenuous activity, so no adventuring!) in a comfortable environment.
What happens to characters who drop below 0 hit points and who do not have access to magical healing will depend on the DM and the style of campaign he wishes to run. A DM who wants to run a more realistic campaign may require the character to have a full rest before he can regain any hit points. One who wants to run a more heroic campaign may allow the character to continue adventuring without penalty. A more middle of the road approach could be to allow the character to continue adventuring, but at a penalty to indicate that he is operating at 0 physical hit points. This penalty disappears after he has taken a full rest.
This system effectively treads a middle ground between the 4e approach of non-magical healing being almost as good as magical healing, and the approach in previous editions of non-magical healing being almost ineffective in the short term. A party that only has access to non-magical healing will have to operate on a narrower hit point buffer, but can still recover some hit points fairly quickly when wounded, and push on.