"How close a person is to death" is a meaningless statement. It carries no information outside of the game state of HP. It doesn't tell us ANYTHING.
I would find it odd if people in 5e who say they are meaningless play that way. If you are hit for 95% of your base HP in the first round by a single attack, does your character react differently than of the hot had been for 1%? If you're down to 10hp do you not use different tactics than if you were at 90hp?
No one thinks that losing hp carries no
game play information. Hussar's post directly acknowledges that it does!
The point is that it tells us nothing about
the fiction, and in that sense is no more of a
simulation than having your king put into check in a game of chess.
Because of the gameplay information, a player might change their tactics. Likewise, because my king is in check I might choose a different move from what I would otherwise perform.
But that doesn't mean that any information is being established about the fiction.
In my 4e game, Miska the Wolf Spider, who started with around 1000 hp, is now getting close to double-digits (or might even be there - I haven't checked my notes). What does this tell us, in the fiction, has happened to Miska?
Contrast how the same thing would resolve in RM, where there would be records of bruising, injuries suffered, etc. There would not just be a gameplay state, but an associated fiction.
And of course, as
@DND_Reborn has posted, the lack of a fiction that correlates to the gameplay state, in the case of hp loss, becomes clear when we look at other aspects of the fiction. For instance as is notorious, even if Miska is reduced to 1 hp of his starting 1,000, that has no implications for how he performs other physical actions. Which fairly strongly implies that, in the fiction, he's not been hurt at all. Yet he's "close to death"! This is not a framework for simulating anything.