So this is how I play hit points. It is not necessarily how you play or how you should play. It's not advocacy so much as explanation. Here is my explanation.
Suppose we have Fighter Bob who is 1st level with ten hit points. We also have Fighter Joe who is tenth level and has one hundred hit points. Now for the sake of argument let us also suppose that they are to an observer identical twins except that one just has more training than the other. Their attributes and musculature are identical.
Now if a giant comes along and does ten hit points of damage what has happened? In the first case Fighter Bob is down and likely dying. He got hit and hit hard and is bleeding profusely. In the second case Fighter Joe perhaps barely turned aside the giant's spiked club and that club managed to create a bleeding gash in Fighter Joes arm. They both took 10 hit points of damage but we might also fairly argue that Bob took more meat damage than Joe took. Joe was damaged though.
So let's assume Bob barely pulls through. So Bob and Joe are recoverying and since they don't have a cleric handy they are both resting and recoverying naturally. If what is healing is the meat, then Joe should recover faster than Bob, right? I tend to suggest that people recover their level in hit points every day. So Joe is fully healed up after a good days rest. Bob though takes ten days to recover. None of this is super realistic but for me it passes the cinematic realism test rather easily. It feels right at a glance.
So to answer your question. I believe if instead of increasing hit points all damage got divided by the targets level the result would be the same. The dividing of damage would represent the skill, luck, stamina, etc...So increasing hit points are a simpler way of doing this division process. All damage is something real. No matter how big the number the result is never zero. The division process is what is represented by the skill, luck, and stamina. The actual hit points would then be the "meat". I dislike the term as even meat is not purely meat. I can stab your leg and stab your heart and the latter will kill you while the former does not. It's the same amount of "meat" though.
So to answer your question. Hit points do not represent intangible factors because they are always tied to the "meat" they represent. If the meat for Joe is 10 hit points just like Bob, then the other 90 that Joe possesses are linked directly to the initial 10. You can't lose some of the 90 without losing some of the ten. You can't recover any of the 90 without recoverying some of the 10.
Hope that clears it up. I hope it also clears up any misconceptions people have on my view of hit points.