
Have you forgotten more about D&D than I will ever know?
Sadly, I have forgotten far less about 1e than I should have.

OTOH, I have trouble retaining things about 5e that I read last week. In the whole Older & Wiser aphorism, the 'wiser' part is more of a stretch goal for me.
(Actually, I routinely accept a lot of what you, personally, say about 5e, because the time's I've cracked a book and checked up on you, you've always been right on the facts.)
What is a "slashing club" but a sword?
Oh! a Klanth?
Anyway, I don't think I know what a "mechanics-only DM" is.
A wargaming-era-style 'Judge' who only interprets rules, to settle disputes between players, perhaps?
I think it's largely accepted that part of what distinguishes a RPG from a boardgame is that the former takes narrative/fiction as input, and yields the same as output, in way that a boardgame does not.
I don't think anything's largely accepted, a consensus, or non-controversial, when you're in an on-line forum. There's /always/ someone willing to offer themselves as a counter-example to any universal assertion, just to tag someone 'wrong' for whatever imaginary points their toting in their head.
There's no meaning of
abstract that makes Gygax's account of hp, or
@Tony Vargas's account of hp, abstract but makes a durability account not abstract.
OR? I'd like to think that I'm a pedantic Gygaxian apologist on this issue, with no ideas of my own, at all.
If you've determined that hp is always meat then you aren't playing hp is an abstraction.
I mean, unless 'meat' is literally taken to the point of an animated pile of hamburger - undifferentiated physical structure that must be destroyed, as hps would tend to represent with a clay golem, for instance.
Yeah, I guess that's another thing: Hit points work the same, mechanically, for PCs, NPCs, and monsters, that last category of which includes noncorporeal entities, macroscopic single-celled organisms, plants, animated lumps of stone or clay or dead flesh and/or bone, fantastic machines, swarms of much smaller things working in concert, conjured forces, whirlwinds & conflagrations from their corresponding elemental planes. Heck, in 3e objects had hit points (in 1e they /generally/ didn't, but made saving throws, but some did, too), and in 4e traps often did (5e, I forget, see above).
So, abandoning my self-appointed role as Gygaxian apologist for whom it's still 1979, I'd have to say that, hps are, necessarily an abstraction, representing many different things that stand between a specific creature and defeat - death for most monsters, destruction for many monsters & objects worth the trouble, banishment/dispelling for a few monsters and spells effects, and unconsciousness & death saves for PCs and those NPCs worth the trouble - so while a 'standard' interpretation that makes sense for PC races might be viable (and couldn't reasonably include supernatural durability without /actually/ getting into the wuxia/anime/Exalted paradigm so often presented as unthinkable when the possibility of giving martial concepts some cool toys comes up), it couldn't ever be universal.