As a DM if I want to ensure PC death, I can always fall back on infinity dragons.
This to me has derailed from “do players want balance” to something else entirely… a complaint about how the game isn’t deadly enough .. or too deadly.
Let’s go back to the original question.
I liked the post that took the DM factor out of it to point out players generally want their characters to be balanced “with respect to each other” so each of them gets a chance to have the spotlight. That is a statement I can get behind, and is entirely different than “balanced with respect to encounters (individually or in series).”
since different folks have different preferences for PC nova frequencies in encounters (every time? Once per 5 encounters in an adventuring day? Never?) we seem to mostly be arguing about how many encounters the dial needs to be tuned to. Which leads to proxy arguments about action economy, the proposed length of an adventuring day, the in practice length of an adventuring day, long and short rest frequency, and so on.
I will stick by my premise that people are psychologically poor at probability and if you tell someone they should win 50% of the time, they think the game is rigged against them unless their actual win rate is 70%. Similarly, tell someone they have a 90% hit chance and their brain turns that into “I can’t miss.” So no matter where you think “balanced” is, my contention is that psychologically, players don’t want whatever that number you might choose is, they want the odds titled past that number in their favor for it to “feel” balanced. This isn’t an indictment of players, it is human nature.
What a DM needs to do to make the players feel the game is balanced is find the sweet spot where failure occurs intermittently to remind the players they don’t have plot armor, but not so frequently they get frustrated. As Matt Colville puts it, “the bad guys don’t know they are the bad guys” and when you get into a fight with them, “they are trying to kill you” (but I in the DM role am NOT trying to kill you, I in the temporary role of the baddies am trying to kill you).
It is one of the things that I feel makes low level play “better” - hit points are low, dice are swingy, and if I am rolling every roll in front of my players, it is likely one of them drops to 0 hp. Rolling in front of them lets them know I am neither cheating “in their favor” (their victory is earned) nor against them (they are not being screwed because I am angry/a jerk/want to “win” once in a while). I am also an advocate for multiple failure states, morale checks so not every fight is to the death, and alternate dight endings like if one of the PCs goes down, giving them an option to surrender, collect their dying, and leave. Any intelligent enemy would prefer to save his resources and allow the PCs to slink off in defeat rather than have to fight to the death. Of course, the se one time the PCs attack, the BBEG is less likely to be forgiving!
In other words, more reasonable villains and less “tactical combat to the death!”
And FWIW, I have found that one PC going down (not necessarily dying) every 4-5 game sessions or so, with death coming only when the party is foolhardy or the dice are particularly uncooperative (perhaps every 5 to 10 times a PC drops the dice might do him in - I haven’t kept track - foolhardy actions are far more frequently the cause… in one case I took the player aside after the session and pointed out several implicit warnings and a couple explicit warnings he had blown past because I wanted to help him recognize the implicit warnings in the future… the explicit ones I reminded him of but didn’t feel I needed to further explain … when I said “this course of action is likely to get your character killed” I wasn’t joking) seems to be about the right amount for players to “feel” the stakes are real without getting frustrated.