Something a lot of people seem to forget when discussing when a character dies is that D&D was designed without a critical hit system. Damage variance was generally small, usually a roll of a die without bonuses. If a monster did 1-6 damage, you knew, from your own hit point totals, what risks you were taking each turn.
When critical hits were added as an optional rule in 2e, they still only doubled the dice of damage rolled, so now there was a 5% chance that monster that did 1-6 damage did 2-12...it added unpredictability to combat, but it was still nothing beyond the pale.
"Death's Door" rules in this time period were more a buffer for low level characters.
3e brought in expanded crit ranges and crit multipliers, but it also did two other things that ended up being massive game changers- critical hits now included damage bonuses, and monsters now routinely had those bonuses. Fighting an Orc was much swingier- he could deal 1d12+3 damage (4-15) per hit, with a 5% chance of dealing 3d12+9 (12-45)! Instant death out of nowhere suddenly made combat unpredictable- if you were a melee character bellying up to a monster, you could go from OK to bleeding out at any given moment, and the humble Death's Door was woefully unable to cope with this.
4e simplified crits by having them only deal maximum damage (though bonus crit damage was a feature of some magic weapons and Half-Orcs, as I recall) and not only expanded how long you could remain alive below 0, but introduced "heal from 0" so that healing at low levels could actually get you back up into the fight, instead of risking someone taking one of the Cleric's 2 Healing Words and still being unconscious. The idea of monsters doing average damage cropped up as an option here, to try and reduce variables further, so characters had some idea of how much danger they were in.
5e went back to "roll double dice" on crits, but some monsters were given lots of dice to throw at people (the Giant Ape's 7d6+6 rock throw is a favorite example of mine). Multiattack on monsters can be seen at fairly low CR's and it's not uncommon to see 3 attacks per round by the end of Tier 1.
Death's Door was buffed again and Death Saves and heal from zero were retained likely to combat this volatility- a character with d8 hit dice and a 14 Con has a fairly predictable hit point total by default (I mean, who rolls for hit points anymore?). By level 7, such a character has 52 hit points. If they find themselves crit by a thrown gorilla rock, the average damage takes them from full to zero, with no opportunity to do anything about it. If the dice are rolled, you could potentially take 90 damage! If our 52 hit point friend was wounded, there's a real risk (if small) that he could die outright! And if he wasn't able to heal from 0, well, lol, he's basically out of the fight and that's that.
People do complain about how hard it is to kill PC's, but it's not impossible, even with all these safeguards. In a world where most people have no real defensive maneuver that still allows them to attack, and only one reaction per turn even if you had one, where monsters routinely attack multiple times and can have explosive critical damage, the possibility is always on the table, especially if said multiattacking monster lays you out with attacks remaining and nobody else in easy reach!
And 5e healing is woefully bad at mitigating this damage, leading to the tubthumping play cycle ("I get knocked down, I get up again") so many revile.*
*5.5 healing is an improvement, but I don't believe it's where it needs to be when compared to incoming damage.
Death at 0 effects are just rude at this point. Sure, maybe if your table plays optimally and everyone has shield/silvery barbs/adamantine armor/bonus action dodge/resistance/etc. etc., it can seem like death in 5e is a joke. That's a consequence of any game that allows players to optimize to take something they don't like off the table.
But the groups I run for aren't like that, and it's a common sight for melee characters to be bleeding out with me wondering if this is the battle that's going to break the campaign. And I'm always happy when it isn't, because experience has taught me that a character dying mid-adventure is not a good thing.
YMMV, of course.
