Mine is a very naive and honest question. Why can't we just live with HP representing only a creature's ability to take physical damage and injuries before dropping? What are the bad things that will happen to the game if we do that?
There are a number of disconnects that occur if you model damage as purely physical damage.
Now, there are models where this works. One approach is an anime-like ability to shrug away and ignore injuries that would be debilitating or even deadly in the real world. This may even be, arguably, the model under which hp make the most sense, but not everyone wants to play an anime themed game.
You could, alternately, say that every injury causes some amount of harm. However, at this point, luck/skill/etc. begin to enter the picture.
Take two 3e fighters, for example. One has 10 hp, the other has 100 hp. They both take 20 points of damage. The first fighter is dead, while the second fighter hasn't been seriously harmed. Now let's assume that that 20 points of damage came from an elephant trampling the two of them. It seems pretty unrealistic that the second fighter was just slightly bruised by
an elephant trampling over him. Therefore, we chalk up the difference to luck, skill, or divine intervention. The first fighter died because the elephant stepped on him, while some factor allowed the second fighter to avoid being crushed. Fighter two may have taken a glancing kick, but he clearly wasn't stepped on like Fighter one was (given that he survives with no crippling injuries).
However, once you've allowed luck/skill/etc. into the picture as above, it's just as easy to allow that some attacks might not connect at all. In some circumstances, it just makes more sense.
Earlier, someone mentioned a character who could skydive without a parachute. IMO, outside of the anime explanation, the only way this can possibly make sense is through luck/divine favor. There have been real world reports of people who fell out of planes and were lucky enough to
walk away. But that was luck. I don't think anyone is going to suggest that the reason that person survived was because of superhuman resilience.
Also think about attacks that would cause serious harm. I'd guess that getting hit with a giant's club could be equated to getting hit by a car. A high level fighter goes up against a giant. Are we really saying that he can withstand the trauma of being hit by a car repeatedly? Even if we say that he's just clipped by the club (sideswiped by a car), he should be in seriously bad shape after a few "hits". To me, it makes much more sense to model the first few "hits" as near misses instead. As for recovery time, luck is an abstract; who's to say it doesn't take as long to recover as a bone takes to mend?
Finally, I'll point out what the system's creator, Gary Gygax, had to say about the matter. To paraphrase him, it's absurd to think that a mid level fighter could absorb as much physical punishment as several warhorses. Hence, a small fraction of hp represents the ability to actually take physical injuries, while the majority represent other factors. If you'd like, let me know and I'll post the relevant (PHB 1e and DMG 1e) quotes for you.
It's not that you can't model hp as purely physical. It's that when you do so, you end up with something very different from the real world or even most fantasy (outside anime). If that works for you that's fine, but some of us prefer Gygax's views on the matter.