It makes almost no sense unless the downed PC is perceivably a greater threat than the ones active and attacking. Right? Otherwise, my monsters are just being vindictive pricks who know they are going to die, and my monsters are generally not like that. They presumably have lives and goals outside of being 1 hp cannon fodder for PCs (yep....I went there 4e...you wanna fight about it?).
If a PC is proven to be a threat out of proportion to the other PCs and is getting back up, then yeah...skewer the S.O.B.
or a pack or horde type situation where after koboldpiling the tough guy down some run to the next target while others savage the body.
or a savage rending situation - thinking gnolls maybe - where a target downed is a wild aggressive mauling prompt/trigger.
The key to this all, in my opinion, is for the NPCs to act appropriately for the setting, the circumstance and their **already presented and foreshadowed** nature.
"They mauled Curt instead of coming for me" should be **expected** when it occurs to the PC and causes PC death, not some sort of forum post rant fodder case of "WTF, that came out of the blue." it should have, IMO, in a well run game be something not unknown, not first shown when it bites (pun intended) a PC with character death. The descriptions of previous encounters should highlight this fact so that the PCs can be prepared for it and take extra precautions. The GM should (to whatever extent he considers balance of encounters) treat this as an extra specially deadly feature the critters have, beyond their baseline stats, as far as "risk to the PC assessments." i would pretty much myself consider this akin to "a favorable terrain" edge in the standard 5e DnD CR setup not at all unlike having the varmints frequent use of a poison that made death saves disadvantaged also be such a factor.
So, to me it boils down to not an endless list of forum edge cases de fury, but to how it is presented within the game, factored into the game, play and story in actual play at a given table to produce moments of greater tension or drama and excitement.
I mean, the first time some medicine check reveals "this poison they used when killing this peasant would among other things make the death saves disadvantaged" (expressed in in-world terms not game jargon), i bet nearly every player/PC would feel their sphincter tighten more than a little before a single HP is taken and that is gaming gold... or at least silver, maybe electrum.