I should think being dead is somehow significant. If that last point of damage - that 16th point if you have 8, or that 8th point if you're only talking unconsciousness - is not more significant, why does it result in unconsciousness or instant death?
Look at your own argument, from earlier - healing from zero to 1 doesn't require any more or stronger magic than healing from 99 to 100, so obviously they cannot represent vastly different changes of state. That's not my argument, but it's something you should probably take into consideration, based on your previous statements.
For the vast majority of people in the real world, you can punch them once and they'll be okay, but if you keep punching them then they'll eventually fall unconscious, and that happens at a different point for different people. There's no real difference between the first punch and the last punch, or any of the punches in between. And it's true for almost everyone, almost entirely without regard for how strong you are. That is Hit Points, in a nutshell.
You can take north of 10x your hp in a-planet-just-hit-you damage and not break bones? And you're worried about what sort of internal consistency, again?
You're the one saying that total HP should matters in describing how a wound of any given damage manifests itself. I'm the one saying that an attack that deals 80 damage (or whatever) manifests similarly on both characters, so yeah, I'm going to say that my version is consistent. Literally.
If you're trying to establish that you can just look at someone and know how much damage they've taken, in hps, non-meta-gamely, how is people with different hps taking the same amount of damage, and having radically different effects from it, not something you care about?
So, you know how you punch a nerd like three times and they go down, but you have to punch Mike Tyson like a thousand times to get the same effect? It's the same thing. You're applying the same amount of force from each punch, but one victim requires a much greater total amount of force to be imparted in order to reach the limit of consciousness.
And do you know what the difference is, between those two people? Some of it is physical health and toughness, sure, but there's also skill in taking a hit, vast disparities in actual experience, and other factors that are difficult to pin down - i.e. much of the same stuff that Gygax was talking about, back in the day.
And, I really have to wonder where this new-found acceptance of profoundly limiting what non-fatal hp damage can represent came from, and whether it'll vanish conveniently later...?
There's rarely reason for me to talk about my personal preference in the matter, because it really
is just a preference, although it's somewhat more-
enforced of a preference since I've been running a 5E game with the default healing rules.
If you want to talk about arrows sticking in someone's back, then it's still consistent, if somewhat less realistic. If it takes one arrow in the back to kill most people, but Boromir can take half a dozen before dropping, then it's the same basic principle in effect. It's just a matter of how fantastical you want your fantasy warriors to be.