It actually doesn't make much difference unless the pc goes down when all of these conditions are true
A There are multiple monsters.
B No matter what makes sense all of them target the player trying to die
C There are enough attacks to drop the player with one attack... force two failed death saves with a second... three execute with a third
D No player is positioned to drop healing word or any other method of healing between first and second or second and third attack. This one is critical and players will eventually begin to count on it as the defacto method of trivializing risk.
Have you tried it?
A. This isn't true at all. You need multiple
attacks, which many- perhaps even most- monsters of even middling CR have.
B. Again, this isn't required. Only one foe needs to focus on the unconscious guy- for instance, one ghoul that stats to devour him- and suddenly the threat is very, very real.
C. I'm not sure what your point is here. Isn't this always the case- that to kill a pc, you have to do a bunch of damage here first? It sounds like you're reiterating point A.
D. Again, this goes without saying.
Of course a pc won't die if someone else can heal them first.
Let's say the party is facing off against monsters with a claw/claw/bite multiattack. Only one monster needs to focus on the unconscious guy to kill him, and it will slay him in a single turn if it hits with two of three attacks. Let's say the monsters all go on one turn, and one monster drops a pc. The next monster in line can probably kill him before any other pc even has a chance to respond; this is one reason why all the analysis about how letting pcs go down and then bouncing them back up is flawed.
In my experience, most people who either complain or crow about how hard it is to kill pcs in 5e simply haven't been in a combat where the dm took the gloves off and gave it a good try. Ruthless play, no giving the pcs a chance to heal the downed guy, good tactics, no fudging the dice to save the party.