This is something that I have been giving a lot of thought on for a number of years as my rpg group in general does not like the loads of hit points school of playing. In particular we nearly always use mooks with low levels of hit pots for most npc. In general only one or two htis are needed to knock them out of the fight.
My current thought on DnD hit points is that the additional hit points above constitution are basically a buffer, allowing the pc to absorb damage, certainly because of experience and skill in line with the dnd next rules. This means that those hits are not actual physical just numerous small nicks and scratches have started to take their toll, just like Conan in the books, or equivilent to using a Fate Point each time you are hit.
The key would appear to be what happens when a character is exhausted after a protracted combat.
My view is this is where constitution comes in. Once you have only constitution points left then you start taking physical, harmful damage. This is the damage that would affect performance and your ability to heal. Anything above constitution would be recoverable naturally after a short rest (This in effect is a healing surge).
Taking this view to the extreme you could allow surprise attacks to attack HP directly, in this way even an arrow could potentially kill someone unprepared with a single hit. Unlikely to happen if full hit points are allowed