Extremes aside it still seems that 4e tried to give some credance to the fact that not all damage was physical in relation to hit points. Luck, resolve and exhaustion shouldn't take weeks to recover from if you didn't have magical healing available.
That is absolutely a reasonable position.
Here is why it doesn't work for me. And saying why it doesn't work to me in no way implies it is wrong for you.
In your first sentence you said "not all damage was physical". In your second sentence you only listed "luck, resolve, and exhaustion". You left "physical damage" out.
For me I'm going to leave "exhaustion" out. HP don't describe exhaustion in my games. But I accept "physical, luck, resolve, etc..." Just call it "physical" and "karma" with karma covering all of the above non-physical.
Now physical isn't "deadly". It doesn't mean a sword through the head. I'll happily describe a "sword through the head "

if it is a killing blow. But for simple HP damage it is cuts, bruises, concussion, strains, etc... A laundry list of things that happen to action heroes all the time and they ignore. I guess it is a little tricky to fully describe in a short text, but it flows very nicely during play.
Karma is even harder to describe. But also actually requires even less description. It just is. It can be as simple a “killing” or “wounding” blow that instead misses altogether. And there is virtually infinite narrative freedom in describing that. But it would be a misunderstanding to say that the “karma” aspect of HP is intended to capture “luck” in its entirety. I can roll a 2 when the hill giant swings his club. And I can describe that as luck. Obviously the hero doesn’t lose any HP for that luck. Farmer Joe has 2HP and the hill giant could miss him. If so, Farmer Joe got lucky. Farmer Joe’s luck has nothing to do with HP, it was just pure luck that anyone could have. Hero Hank has that luck as well. It is always there and it can always fail him. It doesn’t go away and it doesn’t recover.
But Hero Hank also has this “karma”. And when I roll a 14 and the hill giant crushes Farmer Joe’s Head,
Farmer Joe dies. But Hero Hank’s karma keeps his head uncrushed. Maybe he dodged completely out of the way, or maybe he turned and rolled with the blow, taking a massive bruise to his chest. In other words, some portion of the HP loss was “karma” and some portion was “physical”. There is no need to restrict or limit it to one or the other. Either element could be 0 to 100% on a completely open case by case method.
But the point is Hero Hank having a lot more HP than Farmer Joe represents not “luck” or “karma” but a specific flavor of karma that action heroes get above and beyond what the Farmer Joe’s of the world get. And anyone who has ever read a Conan story or watched a James Bond movie can get that.
And everything is rolled into HP. One unit of HP is the same whether it represents come physical damage or it represents karma. And this is nothing new. It is obvious from looking at the mechanics and anyone who reads the 1E DMG should come away with that idea. And it is the same coming and going. Hank’s “Farmer Joe” Karma will be the same every morning. He doesn’t lose it. But his “Hero Karma” recovers at “healing speed”. This is subtle, and brilliant, and excellent.
And the result is that Hero Hank can still have “luck” every day. But if he is the in the woods alone he is going to need a lot of days to be back to 100% from being seriously wounded.
Surges toss this great model aside.