Ahh, Tetra....in 5e terms, a Coup de Grace against fallen opponents is not a

-move.
(not as much of one, anyway

)
That is an antiquated D&D modality....true in 1e & 2e when -10HP was as low as one could limbo, and healing spells were touch based, often healed paltry amounts due to bad dice rolls; thusly frequently requiring multiple spell applications to get someone back to positive HPs.
Of course in 1 & 2e, spells could be disrupted, and the First Aid skill was useful, but not a 5e Healer’s Kit. So a character at -8 HP, didn’t need so much help to die.
For me, 3e with the Massive Damage and Coup de Grace rules, pretty much put out a sign saying that downed characters were fair game, from a system perspective.
When a player can go down to -23 HP, and then up to 9HP from a single Healing Word spell, as happens in 5e, then it behooves the DM to try to
encourage the players to get their fallen up as quickly as possible, without resorting to doing the Death Save Timer dance.
(Earlier editions had the same dance BTW, many groups did not drop all other actions and just concentrate on healing a downed comrade, when the downed player was just at -2 HPs for example).
Wizards are fairly adept at dispatching the fallen- Magic Missile will kill someone outright.
If you are fighting something able to cast MM, your group better get the fallen player back into positive HP territory before the Magic Missile opponent’s turn!
Owl familiars, likewise are highly effective at delivering a Touch Spell Coup de Grace.
Drone strike D&D 5e style.
Quasits and Imps are even worse news.
Incorporeal Undead are also very good at this. Shadows are low CR, and a Wraith, even in it’s 5e form, will scare the

out of downed player when, in additional to having 2 failed Death Saves from the Critical Hit
Life Drain attack on the unconscious player, their maximum HP total is also reduced. Which of course could lead to a massive damage death, from this alone.
Legendary Actions can also excel at putting the Death Save pressure on, especially if the downed character
failed their Death Save on their turn, and then the DM uses a Legendary Action to whack the downed player.