How big is your group. Imagine a group with sayyy.. a fighter a paladin a druid a bard and a celestial sorlock. Nearly every PC has healing word, a healing word analog with a different name or a very similar thing like 1hp LoH. Simply targeting a downed PC doesn't work if the first attack needs to hit->drop the pc ->second attack fail 2 death saves ->3rd attack kill. Players have AC & hp enough to not worry much just starting a fight& by the time one can drop the foes are probably down a few. If even a single player has a turn before the third attack lands the whole process is likely to reset with a tiny heal+ the damage that got nullified by death saves on those first two attacks or the next two worth of HPI hear this enough that it must not come up as much in other peoples games, but healing to single digits, while it makes the player useful, is often more dangerous than being unconscious. I’m not big on targeting unconscious players, but I do have to go after anyone standing and single hp territory is where a failed save or monster crit could be massive damage and not leave you any death saves.
edit: it comes up so often because it's so blatantly metagameish gamism in ways where the only meaningful counter is a gm load heavy mass combat pretty much building an encounter to blatantly execute a pc
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