The trouble is that this is simply wrong. No offense, You're right that this is what the D&D rule books have always claimed were happening when hit point damage was taken.
But they were wrong too.
There are simply too many "corner" cases where the claim that no physical damage was done is demonstrably false, or utterly at odds with physics.
Most blatently falling damage. I had a dwarf back in 2e with 125 hitpoints. Falling damage capped out at 20d6. Unless he was already wounded a fall simply could not kill him. He could skydive without a parachute, and he knew it. "luck" cannot explain that.
Poisoned or diseased weapons are another test. Every hit demands a save, ergo every hit had to break the skin and introduce the toxin into your blood stream.
Tie a guy to a post and shoot arrows at him, drop rocks, stand in a fire, etc. Build enough "corner cases" and there's no room left in the center.
It works the other way too, btw. In theory any wound is at least a point of damage, but I could be covered with small animal bites and not noticably closer to death, yet I don't think I have any great ability to soak damage. I do not want to take a baseball bat to the head, yet in D&D that's only, what, 6 or 8 points of damage? I've had easily more bites or other minor wounds than that on a single bad day at the zoo. Still not dead.
So, yeah, hit points are not a great damage modeling mechanic. But they are simple, easy and fun. But pretending they have no actual in game existence is pointless. The best 'in game' explanation I've ever heard is that HP represent your souls ability to hang on to your body, even when it might normally have let go. Between resurrection, gods, speak with dead, etc there is no doubt that the soul exists in D&D. I see no reason why you can't run with that explanation even for a 'mundane' class like a fighter.