The first question to ask is: what is any instant death rule hoping to achieve?
The answer would be: to add danger to every combat - to remove the game from "routine" combats where there is practically no risk. (And the reason for this would be to have players hesitate to solve problems with combat).
But is this really appropriate for S&S?
I would argue, no, it isn't. It might be appropriate for a low fantasy game such as Warhammer. But S&S is not that genre!
I'll circle back to this later in this post. Let's now instead examine the printed motivation of the player's guide:
In sword and sorcery stories, the protagonists regularly kill their foes with a single well-placed hit. Altering the instant death rule makes it possible to simulate such scenes. But it also makes combat much more deadly for the player characters!
But the instant death rule as given adds
nearly zero insta-kill chance, once characters are off the very lowest levels. All it does is add a
considerable risk of not just dropping unconscious from losing all your hp, but never waking up again. While that is a worthwhile goal in itself (and indeed is strived for by many rules systems), it is arguably not appropriate for S&S
games (as opposed to novels), and it is not what the stated design intent says.
I would argue the way to achieve the stated design goals would instead to feature a constant small probability of "killing blow" to every attack. For instance, make a Fortitude save after each time you've been hit by a large attack (where "large" is defined by your constitution and level). But of course that's just loads of more rolling. There already exists a suitable criteria: critical hits.
A more functional instant rule would say:
Instant Death: A character dies when the enemy scores a critical hit where the weapon die scores great damage.
For daggers and other d4 weapons: when a 4 is rolled. (25% of all crits)
For short swords and other d6 weapons: when a 5 or 6 is rolled. (33% of all crits)
For long swords and other d8 weapons: when a 6, 7 or 8 is rolled. (37.5% of all crits)
For halberds and other d10 weapons, when a 7, 8, 9 or 10 is rolled. (40% of all crits)
For greataxes and other d12 weapons, when a 8, 9, 10, 11 or 12 is rolled. (41.6% of all crits)
For ease of use, write down the needed instant death damage die result on your character sheet. For example, if you wield a battleaxe in two hands (a d10 weapon in that configuration), you'd note "Instant death: 7+" on your character sheet to remind you any critical scoring a 7 or better would kill your opponent.
For example, a character is killed if an attack with a battleaxe scores a critical and rolls a 6 on the weapon die. His level doesn't matter.
This would be a rule in line with its design intent.
---
That said, the overarching question remains: is really instant death appropriate for a S&S game?
I would argue that no, it isn't. During any D&D campaign (S&S themed or no) player characters have many many combats. There really is no way to avoid them, and indeed, D&D is predicated on the assumption that combat is an exciting reward and centrepiece of any campaign, not some very risky business best avoided.
So I would suggest instant death should only apply to non-notable NPCs. Mooks.
But there already exists a sufficient mechanism to distinguish NPCs from heroes - the basic fact that (most) NPCs are simply considered dead at 0 hp and removed from play.
I would highly recommend that the thinking behind instant death ideas are instead redirected towards magic use. I would argue "constant risk of usage" is much more thematic and appropriate for the Sorcery halve of Sword & Sorcery.