Aren’t you kind of overlooking the one big thing in the D&D rules that DOES account for for off-book propositions?I'm half with you. The knife to the throat situation is a problem, but on the other hand I don't in any fashion think it applies to the sniping scenario the OP describes.
The knife to the throat objection is one of the classic objections to the D&D rules and hit points specifically.
D&D's abstract hit point system depends on the stakes of an attack not being known until after the attack is made. For any proposition to attack, the exact nature of the attack (how it is described) is not known until after the fortune is described and the hit points that are inflicted are compared to the hit points of the target that remain. The resulting wound (if any) is then described in terms of the proportion of remaining hit points that the attack removed from the target. Thus, a 4 hit point attack on a 40 hit point target is described in an entirely different way than an attack on a 4 hit point target. One results in some minor wound, while the other results in a potentially mortal wound - even though on paper they both did 4 hit points of damage. Four hit points of damage means nothing in terms of fictional positioning except relative to the hit points of the target.
This sort of system is generally known as 'Fortune in the Middle': proposition->fortune->interpreted results.
Where this system runs into problems is if somehow you can arrange to have the stakes of the action be assumed to be known by the participants before the fortune roll is made, a situation normally considered to be Fortune at the End. In systems built for Fortune at the End, the game rules arbitrate between two outcomes in some manner, with high stakes like the death of the opponent normally being quite difficult unless the attacker can achieve equally great advantage. But if you can arrange this or if it happens in the fictional positioning of a D&D game, then the abstract system comes apart because it will generate a result incompatible with the assumed stakes. Remember, the normal fortune attack roll does not know what the stakes are. So naturally, if you begin an attack check by setting the stakes, the fortune system will not be able to arbitrate between these stakes and decide what happens.
Falling is one common example of this. When a character falls it feels like we know the stakes before we roll. We already know that the player has fallen from a great height and to a very large extent the circumstances of the fall or we wouldn't be rolling for falling damage. So there is relatively little opportunity to narrate away that fact. When the abstract fortune system then deducts hit points from the character it frequently generates a result that doesn't feel right for the narrated fictional circumstance.
The knife at the throat example is another classic example. In this case, it again feels like we know the stakes before we roll - the throat is going to be cut. So when we ask the abstract fortune system to resolve this as an attack, it generates results that don't feel right for the stake we set. We are wanting a system in this case that tells us what the result of someone's throat being cut is, but the D&D rules don't do that. In no way did we plug into the system the situation. Of course it doesn't handle what we wanted, it was never designed for that.
D&D from the very start has always held as an exception to the normal combat rules that if the target is truly helpless to resist an attack that the normal combat rules don't apply. In 1e AD&D this wasn't even a fortune test. The stakes simply occurred, throat cut, because there was no reason why they shouldn't occur because the outcome in that case was not doubtful. 3e D&D codified this idea as the Coup De Grace rules. If the target was helpless, then a different fortune resolution system applied.
But this still doesn't address the 'throat to the neck' scenario, because under the D&D rules someone with a knife to their throat isn't helpless.
One of the most important things to note in this scenario is that the D&D rules have no way to generate the fictional positioning of the scene in the first place. That is to say, nothing in the D&D rules tests the proposition, "I [try to] put a knife to the target's throat." One of the most important things to realize then is that the proposition, "I put a knife to the throat [of a creature that is not helpless]" is an invalid proposition under the D&D rules. D&D has zero ways to handle that proposition and zero tests of propositions that result in the fictional state 'I have a knife to non-helpless target X's throat'. The stake that the player wants to set can't actually happen in the game, and if for some reason a DM does pass that proposition and use some sort of fortune test to indicate that fictional positioning has transpired, then the DM has erred and not the game.
We can imagine the sort of things that first have to happen before anything equivalent to this fictional positioning could occur. First, the PC would have to win some sort of grapple contest in a definitive manner, so that the target is in a state like 'pinned'. But the 'pinned' state is by the rules not a state of being helpless, therefore the 'pinned' character does not have a knife to the throat. Rather, the state described by the rules is much more like the fictional positioning sometimes seen in movies where the attacker is trying to push a knife into the throat or vitals of someone that they are grappling with, but the person is holding back the knife arm preventing the attack. In this contest, damage is equivalent to slowly pushing the knife into the targets throat while they resist vigorously, a state that will eventually but not immediately result in the targets death. But you might argue, what about the case where the knife blade is already held against the throat and the position of the defenders hands is already known. Well, again, this fictional positioning cannot result from the D&D rules, or at least, not without the cooperation of the defender who must agree to voluntarily be helpless.
The objection can then be made of course that this not realistic. There ought to be situations where an attacker can achieve the fictional positioning of a knife held to the victim's throat. And this objection is completely valid, but at the same time it's not at all clear what can be done about it. If you have some rules that allow a victim to be made helpless and thus bypassing the normal combat mechanics, then that is a very powerful form of attack and you can expect most combats to evolve toward that as a meta-strategy. It's easy to complain that the rules that don't let the normal hit points be bypassed generate stupid outcomes, but the problem is that any rules that do allow the normal hit points to be bypassed are also likely to generate stupid results. For example, if you had rules that allowed a grappler to make the target helpless, and then allowed the grappler to perform a coup de grace as an immediate action, then the upshot of those rules would be grapplers would be extraordinarily powerful. A PC classed grappler NPC would likely be devastating.
I find that players get a lot more thoughtful about combat house rules when they realize that the same rules that they are proposing will be applied to them. This has a tendency to give the players a large incentive to ensure that the rules are fair and balanced and make for a good gaming experience, and for that reason if no other, I would encourage DMs to resolve actions by NPCs with the same rules you use for PCs. If you have players that know that whatever good things that they accrue for themselves under the house rules, they'll never have to pay any price for those rules, then you'll end up in a situation where players have an incentive to play the metagame and try to agitate for and lawyer for house rules. "When the rules generate stupid outcomes, the rules are wrong" is a powerful and very disruptive tool in the hands of a power gamer if it is applied in a one sided fashion.
This is why the game has an arbiter. The DM is the game’s rule system that handles these cases. A human being with a brain and judgment who isn’t mindlessly adhering to program but weighing stakes and potential outcomes in advance of asking for a check.
So, respectfully, you’re wrong on this claim: “D&D has zero ways to handle that proposition and zero tests of propositions that result in the fictional state 'I have a knife to non-helpless target X's throat'.”
Moreover, re: helplessness, under my “checkmate” houserule, helplessness isn’t a prerequisite. Helplessness certainly does qualify for checkmate, but it’s not the ONLY thing that qualifies. Circumstances may permit other conditions that permit automatic defeat.
Take a fight on a rope bridge, where some participants sever the ropes - that’s an automatic loss for anyone left on the bridge when the thing shakes loose. You know the rules of d&d don’t cover that scenario either. The creatures on the bridge aren’t helpless, can defend themselves, may have full HP. But the human brain of the DM can elect to apply some rules like figuring out how many HP a rope bridge has and calculating fall damage or not. They don’t have to - they could just as easily rule that anyone on the bridge falls and the combat is over. Or they could ask for a strength check to cut the ropes. Or offer a save to the creatures on the bridge. Or, or, or...