For sure, but I think this is more than a binary of "do you attack downed PCs or not?".
I think this crosses a line because it's an auto-kill with no warning if you treat it as three separate sources of damage (which WotC have wavered on).
A monster attacking a downed PC still makes attack rolls against their AC, and I think even if monsters can target downed PCs, as per your session 0, they often - it would often be unnatural for them to.
This is more like:
1) Never attacked downed PCs.
2) Only downed PCs when it makes in-character sense for the monster to do so and isn't a guaranteed one-round kill with no rolls.
3) Only downed PCs when it makes in-character sense for the monster to do so - differs from the above in that you don't pull punches but you do RP the monsters correctly (about 10-20% of DMs do not really RP monster behaviour in my experience).
4) Full Tactics RPG/boardgame approach, so RP/in-character behaviour is secondary to what makes tactical sense.
My feeling is most groups don't discuss this in session zero but are unconsciously operating on 1 or 2, and 3 would seem like a line cross. 4 is always going to be immediately obvious from the first session at least, even without a session 0 - my experience type 4 games have about 5x as many arguments/"polite discussions" about the rules and their interpretation as other games. My personal experience is that they're weirdly popular with DMs who aren't very good at D&D's rules, which is um, vexing (I saw this a lot in 3.XE).
One other thing to consider is consistency. If you do treat this as three separate sources of damage in this very emotive situation, you have to be absolutely sure that in every other situation you count MM similarly, for better or worse.
Personally my default is that death is never off the table while also recognizing that as DM I can always kill off PCs if I want to. Much more fun to have that animal that attacked the group to retreat with the unconscious PC in tow rather than killing them outright. Unpreventable and unavoidable death is rarely fun, although of course individual mileage may vary.