When you say that each individual HP must contain some portion of physical damage, you are committing the Fallacy of Division. Correct that.
In order for the Fallacy of Division to apply, there should be evidence that it is indeed false. That is, there should be an example of the 5e PHB/DMG/MM not treating each individual HP like it contains some portion of physical damage. In fact,
many examples, enough to pass a threshold of simple error. That would show that the idea that each individual HP must contain some portion of physical damage is, indeed, not the case.
Such evidence is
critically lacking. Any effect that recovers HP can easily be interpreted as if it contained some measure of physical healing. There's been no serious attempt to show otherwise. The closest one gets seems to be indicating that healing during a rest cannot be totally physical and stay "realistic," but even if one grants that point, that point does not show that there is no physical element to healing during a rest, merely that it is not 100% physical, which is well within the interpretation of hit points as being
part physical.
So I'm afraid you must correct yourself and your cavalier use of the world "fallacy" in complete absence of evidence of falsity. Or, to put it another way, you are suffering from the
fallacy fallacy.
Don't get me wrong, 5e could've made some other choice, or could later present some view of HP that isn't consistent with that, and it would be "fine." And nobody cares what anybody does at their table or if there is an ounce of "officialness" to it. There's nothing binding WotC or individual players to this concept. It is simply the case in the rules as they exist now. What appears baseless wishful thinking is the idea that you already have HP in 5e treated sometimes as if it was not in part physical. There's no evidence for 5e using HP in that way. You can interpret it that way, but there is no problem with
not interpreting it that way, and there's no instance of the game itself using that interpretation. Which means that any attempt to insist that one is
doing it wrong by including physical damage in instances of hit point recovery or loss is clearly absolute hooey.
And, again, what brought this up in the first place what a poster's desire for explanation: they wanted to know why someone could find this inconsistent.
And the reason someone could find this inconsistent is that every other instance of gaining or losing hit points in the game can be interpreted as at least a bit physical without any contradiction, so an element of gaining or losing hit points that is not at least a bit physical
is a contradiction.