Agreed.
However it's something the game has, sadly, never modelled very well at all.
Case in point.
A character at 1 hit point, unless one is all it ever has (which I don't think been possible since 1e), is about as close to being dead as it can be without in fact being dead; and thus should not be capable of doing everything as well as when it's at full health. But the game's never gone into this much detail, leaving us with a much-too-binary system of you're either fully functional or you're dead.
The 1e-2e solution of death at -10 and the area between 0 and -9 being a range of lessened functionality (or just unconsciousness, but even that's still too binary) actually solves a surprising number of these headaches. But for some reason 5e doesn't want to track negative hit points, and so out the window goes that design opportunity. Couple this binary on-off situation with a) an inability to go below zero and b) in-combat ranged healing and you've got Whack-A-Mole, which is truly ridiculous.
I'm sure it does, and all's well as far as it goes.
The problem is it's the rules themselves surrounding this that need help; and my point is they do need to be changed. Not just death-and-dying rules but the whole resting/healing/recovery paradigm, never mind the relationship between hit points (as a percentage of one's maximum) and health and-or functionality.
4e - an edition I rarely praise for anyhting - was on the right path with its bloodied mechanic: go below half your max hit points and something or some things changed. There should also be changes at the 1/4 point, at the 1/10 point, and at 1 h.p. if you've 20 or more maximum; to reflect generally lowered functionality and - with some classes - increasing desperation.
Instead of looking at the raw number, look at the current h.p. as a fraction of the character's maximum.
Someone at 1 h.p. and whose maximum is 1 h.p. is as healthy and functional as they're ever gonna get (and one can make a fine argument for that being not very, but that's another discussion). But someone at 1 h.p. and whose maximum is 100 h.p. has been beat to rat-scrat and is, compared to normal, close to death. And this is true whether you see hit points as meat, as plot armour, as luck, or whatever: someone at 1 out of 100 is in bad shape.
Put another way, I see someone who's at 3 out of 6 as being, to an outside observer, in approximately the same condition as someone who's at 50 out of 100: they're both down about half their total.
The fact that not only has D&D ever modeled this, but that it has not even meaningfully attempted to, suggests to me that it's more likely that it is your interpretation (that someone with 100 HP at 1 HP has been beat to rat-scrat) is not the intended one. That isn't to say that you're wrong for wanting to interpret it that way. Just that, under scrutiny, it makes no logical sense that if someone can function as well a 1 HP as 100, that they can reasonably be interpreted near death.
4e's bloodied condition is, as you say, more than most editions have done to model it, sure. However, it's clear that bloodied is not intended to represent nearly dead, as it carries no actual penalties but rather simply functions as a trigger for various abilities, both good and bad. I actually still use bloodied in my 5e games, even though it has no mechanical impact in this edition. When an attack bloodies a creature, I describe it as being bloodied by that attack in some relatively minor way, and this clues in the players that the creature is about halfway to 0. Attacks before and after (which don't take it to 0) are described as attacks that should have hit but for a last second dodge, unless they carry an effect that requires contact in which case I describe it in a minimally injurious way.
The closest I can think of actual "nearly dead" status in D&D is (I think) from 1e (I might be mistaken though). IIRC, if a character goes to 0 HP and survives, and recovers without magical healing, they are out of commission until they are able to rest for an extended period of time. Going off of memory, they can follow their allies and speak, but can't fight or otherwise use any abilities, and if they receive even a single point of damage it automatically kills them outright. Note, however, that prior to going to 0 they are fully capable at 1 hp. It is only after recovering from 0 that they are beat to rat-scrat. Which logically implies that there are at least two different ways of defining 1 HP in the fiction of 1e (or whichever edition I'm thinking of). One where you haven't gone to 0 and are mostly fine (possibly a little worse for wear, but not in any way that should meaningfully impair you), and another where you went to 0 and are beat to rat-scrat and cannot meaningfully do much (you are seriously impaired).
If you want to institute penalties at 1/2, 1/4, and 1/10, that's up to you (and your table). However, the simpler solution (IMO) is to change how you describe a character at 1 HP, in which case such rules changes (and the death spiral that usually goes hand-in-hand such changes) become unnecessary.
"Do not try and bend the spoon, that's impossible. Instead, only try to realize the truth...there is no spoon. Then you'll see that it is not the spoon that bends, it is only yourself." -Matrix
YMMV
