To be honest, I'm always surprised when I read comments to the effect of "Hit Points only represent physical damage." No offense, but this is patently absurd - and in any edition.
Take, for instance, AD&D 1E. An ancient red dragon, one of the most feared opponents in any edition of D&D and a creature presumably weighing many tons, has 88 HP. A 7th level fighter (yes, 7th) with an 18 CON can have 98 HP. Think about that for a moment. There is simply no way that a medium (mortal) humanoid of any level can withstand more physical damage than an ancient red dragon. I would suggest that in all but the rarest of instances, a medium sized creature shouldn't be able to withstand more physical damage than a large creature, that physical damage capacity is a function of a variety of factors, including size, body density, muscle mass, thickness and hardness of skin, etc - most of which simply doesn't factor into a humanoid creature, and certainly would not increase (much) with level.
Later editions of D&D improved this monster-to-character HP ratio somewhat but in every edition, the ratio of character HP to monster HP has been absurd (if we take it to be merely physical damage capacity, that is).
I am not saying that in D&D Next, HP should not more closely represent physical damage and even physical damage only, but that is not how any edition of D&D was designed. Or, if it was designed that way, it was a flaw in the simulationism of the game.
To answer the OP, I think the reason it has represented things other than physical injuries is that it is simply a gamist mechanic that allows for a kind of epic, cinematic quality that has always been part of D&D combat. In reality, taking maximum damage from an attack would imply death - if an orc critical hits someone with an axe, doing the most damage it can possibly do, anyone should die - that is, if we're going for a realistic game. But in actuality, HP are an abstraction that represents the capacity to withstand attacks before dying, which of course includes the bodily element. AC, then, represents the capacity to prevent attacks, but once they "get through," HP are there to buffer actual mortal damage.
In truth, the AC/HP mechanic is awkward and rather unrealistic - they over-lap a bit and AC really should go with something more akin to body points. But the bottom line is that they work; they are fun.
This is not to say that it is "badwrongfun" to consider HP to be body damage only, but that it is an incorrect interpretation of the rules-as-written, and thus akin to a house rule, and one that actually makes very little sense. Hey, but we're talking about a fantasy game, so have fun with it! Let's just call a spade a spade and recognize that it is incredibly unrealistic and not what the rules intend.
All that said, there is no reason that the abstract nature of HP couldn't also include a physical component that represents at what point a character actually sustains physical damage. There are a couple ways to go about this without adding undue complexity to the game, one of which would look like this:
Have some kind of "physical damage threshold" that represents at what point, of a character's total HP, they start taking physical damage. This could be similar to 4E's "bloodied" but really mean it and, I would think, be much lower than half. Depending upon what 5E's HP scale looks like, I'm thinking the Constitution score X a size multiplier (e.g. x1/4 for tiny, x1/2 for small, x1 for medium, x2 for large, x5 for huge, x10 for gargantuan...or something like that).
In addition to the above, as a deadlier variant of the core game, critical hits could always do damage to the physical body. This could obviously be quite deadly, so I would suggest that it be an optional rule. Perhaps, also, it could include some kind of saving throw to see if the damage actually "gets through."
So, for example, a 1st level fighter with a 16 CON would have 16 Body Points and, say, 17-26 total Hit Points (or d10 above that, although I would suggest that if HP are rolled, there should be some rule that allows a player to "take half" of their max HP increase if they roll low, so the range at 1st for this fighter would actually be 21-26, or CON + 5-10). Let's say that at 11th level, CON has been increased twice to 18, so the character has 18 BP and 73-128 total HP.