The whack-a-mole style gameplay on 0 HP PCs is an unfortunate inheritance from the tabletop, though Larian makes it even more forgiving by not having critical hits lead to two automatic failures rather than one.
It makes some degree of sense to safeguard the player against bad RNG and Larian's sometimes bloated encounter design.
As for adjustments for higher difficulties, maybe. Many DMs make death saves stick until the next long rest or, in particularly gritty settings, hand out a level of exhaustion each time a PC is downed.
