The problem is, this assumes us players have no problem with monsters hitting the defenseless and fallen.
I certainly sympathize with your position, myself hating the idea that monsters should keep hacking at fallen party members to maintain the game's deadliness.
But it's the best way for monsters to win. Surely you don't object to monsters trying to win?

Edit: It still doesn't make 5e a deadly game - PCs just cast Revivify after the fight. Permanent death
IME is almost always due to PCs losing a fight & fleeing, leaving some behind on the ground.