I think you got me backwards there: I was saying that if people aren't bad at tactics, they will realize that dropping to 0 is a bad idea. If they DO care about the story, you don't need to 'punish' them extra for falling to 0. I don't think players can abuse this... I just don't think it's in any way the solution to the problems "My players think dropping to 0 is a good tactic" or "My players don't give a damn about whether their characters live or die".
I am saying that people caring about story does not mean that rules can't also fit the world you want. Back to my world as an example, my players are almost 100% story driven. So, I make rules to help tell the story I want to go with my world. There is no story disconnect when the mechanics don't fit.
Story: A lot of gods died, most importantly every single one of the Nature gods.
Rule: No Nature Clerics (As champions of a god anyway, you could still play one, but call it a Druid instead.)
Story: Plane of Death has a separate, very slow, time progression, and is freezing cold.
Rule: Anyone who dies wanders a Blizzard for centuries-per-second, so if they come back their Soul remembers that cold. Cold based issues occur, and stack as they die more often.
Story: Most magic is Chaotic, borderline uncontrollable.
Rule: Most Full-casting classes cannot go higher than level 12, as the higher magics are outside PC control. Though, I might consider some sort of artifact that allows casting a higher spell, with a spellcasting check, or a Con save to avoid some sort of detrimental effect. Something like a Legendary Scroll maybe.
All of these rules help tell the story I want to tell, and helps my Players better picture the world they are in from the character's point of view.