I will try to explain, but I am don't know that I have the ability to clearly and fully do so. I know I can't explain my point as thoroughly as you do yours!
My understanding is that "Vitality"-type systems, including standard D&D HP, refers to the stuff you can burn up easily without suffering long-term problems. It's the "luck points" as opposed to "meat points", to use the perhaps trite terms a lot of people use for this. Being dropped to 0 HP puts you on a timer, but you have resources that can be expended to pull you back from the brink. Those resources are "Wounds", and you can't recover those swiftly or simply. 4e is somewhat different in that you can do one-way conversion of "Wounds" into extra "Vitality", but otherwise pretty much in line with any other such system.
I can't speak for other systems or how other people use them. I have never played in a system the had separate pools for wounds and vitality. Though we had heard of them, we just made a system that works for us. I say this just to let you know I am not speaking about other systems or other viewpoints or other experiences with VP & WP (HP & BHP), just our own.
For us HP are:
An abstraction of a creature's luck, divine favor, stamina, ability to take minor physical injury, and mostly skill. You get more HP as you level primarily because you are more skilled at avoiding serious injury. For us healing surges (we use HD now) are, in large part, the stamina portion of that formula.
So for us, HP is not simply luck points.
HP is a creatures ability to avoid serious injury. This can be physical (thick skin), celestial (a god's favor), stamina (attrition, recovery, etc.), or skill (combat/adventure training aka levels).
In some ways, the standard HP and surge recovery of 4e is more lenient, but in other ways much, much less so. Your BHP can be recovered by magic--quite easily, in fact. A single casting of cure wounds, even at level 1, has a better-than-even chance of doing so (2d8+3 averages 2x4.5+3 = 12; you'd need to roll a small but noticeable amount below average); cast by a Life Cleric, it's almost guaranteed to do so (2d8+6 averages 15; you'd need to roll the lowest or second-lowest result.) If upcast, even a single level, it functionally guarantees BHP restoration (4d8+3 averages 21)--meaning a single day is enough to restore most lost BHP, if the party healer spends it doing nothing but casting heals, unless you reduce the rate of spell-slot recovery to match, at which point all you've really done is rescale the timing so the whole campaign moves at a slower pace, but the per-session timing wouldn't meaningfully differ.
To be honest we hardly ever come across magic healing. My group has no magic using healers (the only magic user we have is a Wizard). So most of our HP healing is through spending HD or rest, and healer's kit, medicine checks, and rest for BHP. Sometimes I may throw them a potion or too. We play in a low magic setting.
So I don't really care if magic makes it easy to heal. That is the point of magic IMO: make difficult/impossible things easy/possible. If a cleric is using a bunch of spells to heal the party, that is working as intended IMO. I don't understand why this would heaving be an issue.
OH, I did forget that magic healing requires you to spend your (the recipient) HD. I took that idea from 4e. Like I said, we rarely come across magic healing!
This might be a good time to explain that PCs can spend HD on a lot of things. Here is a snip of our basic HD rules, though we make things up as we go along too:
The one and only part that isn't there is the "this literally makes something cease to function", and I just...I don't really see what value that has? Like I'm genuinely unsure why having BHP which achieve that thing is...a thing you want to do. Having 0 HP already means the function of something is in danger of ceasing. Being dead already means the function of something has stopped. I don't see what is added by having this...other track of death?
It is the only track of death in our game. 0 HP has no mechanical effect except you gain 1 level of exhaustion and any future damage goes to your BHP (until you recover some HP).