The knife to the throat objection is one of the classic objections to the D&D rules and hit points specifically.
It is, but 1e, at least, wasn't /as/ susceptible to it - if creatures were "sleeping or otherwise helpless," I think the phrasing was, you could kill them at 1/round. No CdG or anything.
If the DM takes the knife-to-the-throat scenario as helplessness, it was taken care of.
But there's one huge, unspoken assumption in that scenario...
D&D's abstract hit point system depends on the stakes of an attack not being known until after the attack is made. 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. <snip Forge jargon>
That is to say, nothing in the D&D rules <resolves the action declaration> "I put a knife to the target's throat."
The assumption is that you can get a knife to the victim's throat without first either reducing it's hps to the point that said knife is a threat of near-certain death, or rendering it helpless.
First of all, in genre, a knife to the throat very rarely results in a protagonist or named baddie getting his throat cut, let alone fatally cut. So it's hard to count this as too big a failing of the system, for that reason. OTOH, in genre, very often, that sort of standoff will end with the character who has the drop being momentarily distracted and the victim getting away, with combat or pursuit ensuing from that point. Hps also don't do a bad job there - that's a perfectly fair way of narrating the threatened attack being resolved as a miss or some damage to the hostage and move on from there.
What D&D doesn't handle so well is the standoff scene, itself. The threat of combat isn't much of a motivator, since combat resolution in D&D is a pretty significant chunk of the game's fun potential. It could work with a low-hp, helpless victim the PCs care about, of course (but the players caring about an NPC is an up-hill battle in a lot of groups).
One system I recall handling such scenes way back when was Hero, I don't recall which game it was, probably Danger:International, but it introduced a 'covered' mechanic. You'd make an attack, and, if you hit, instead of resolving damage, declare the target "covered." Then you could make demands with the damage from the hit held in abeyance as your threat. The target or an ally - or unsuspecting interloper - could create a distraction that would end the covered standoff and the target wouldn't take the damage, combat or whatever could resume.
That /could/ work in D&D, in situations where the damage from the attack - like an assassination attempt, perhaps, or a regular attack if you're already low on hp - were a credible threat.
Of course, it may not be a standoff scene, but a denouement as a defeated foe is forced to wrap up the last dangling plot lines. (4e inadvertently addressed that in an off-hand way, when it expanded being dropped to 0 hps to say that the attacker could describe that you he liked - so it /could/ be unconsciousness, or surrender, or holding the defeated foe at sword-point, or whatever. But that implies that, if, you want to do the knife-to-the-throat thing, defeat the enemy , first.)
