It's becoming clear to me that part of this debate touches on two fundamental things:
1) What hit points are.
2) What the rules do.
For the first one, the idea of killing one's self with a rusty dagger or putting a plasma cannon to your head and pulling the trigger shouldn't be handled by ablating hit points as you would in a combat or anywhere else the outcome should be uncertain because the PC is doing what they can to survive. Under normal circumstances, they're trying to survive and the dagger strike, plasma cannon shot, or falling damage is a stroke of luck that does a measured amount of damage that the character, due to their game defensive power "hit points", may survive. But there are, reasonably, times in which they shouldn't apply - such as the aforementioned suicide attempts as well as ridiculously deadly things like putting a head in a guillotine.
For the second one, there are times when having rules that putting your neck in a guillotine and dropping the blade is fatal shouldn't be necessary. This is outside the rules of the game because it's unreasonable for the rules to even attempt to be this complete in simulating a reality. The rules exist to operationalize the actions a PC may take in the game that fit within the genre being simulated and serve as a guideline for how to resolve the action when the end result is in question - not define the whole of the setting's physics or possibilities. I think it's entirely reasonable for a PC throwing themselves off a cliff for neither necessity nor through the fickle whims of fortune to fall into the category of something outside the expected bounds of most genres - and thus not necessarily subject to the falling rules. It may be appropriate in a superhero game where notoriously invulnerable PCs are known for landing hard and, often, intentionally as part of a necessary and calculated act (notable examples include Thing, She-Hulk, Wonder Man, and Colossus), but those are somewhat loaded examples as those characters have high degrees of superpowered invulnerability.