How is it decided whether a creature can survive without a head?

Question

The vorpal sword has the property (emphases mine):

When you attack a creature that has at least one head with this weapon and roll a 20 on the attack roll, you cut off one of the creature's heads. The creature dies if it can't survive without the lost head. A creature is immune to this effect if it is immune to slashing damage, doesn't have or need a head, has legendary actions, or the DM decides that the creature is too big for its head to be cut off with this weapon.

A creature dies if it can't survive without the lost head. It is immune to this if it doesn't need a head. Those are both pretty clear conditional statements. My question is how are these decided?

The description tells you
D&D is an exceptions-based game. We begin with the assumption that creatures cannot survive without their head. Any creature that can survive without its head will have that feature noted in its description. For example, the description of a troll (both in the lore, and the 'loathsome limbs' variant sidebar) says that it can survive without its head. The description of a hydra (in its stat block) says that it can survive the death of all but its last head.

OR

The DM decides
Rule 3: "The DM narrates the results of the adventure's actions." If PC's cut off a creature's head with a vorpal sword, the DM decides, based on how they have presented that creature and its fantasy biology in their game, whether or not the creature survives.

Problems with 'The description tells you'
If we start with the assumption that 'creatures cannot survive without their head unless their description says otherwise', why do we have that assumption? It is not stated anywhere in the rules. It is a pretty reasonable assumption that most creatures cannot survive without their heads - but if we limit our cases of survivors to only those that explicitly say so, we are excluding a lot of pretty reasonable cases.

Ettins, for example, seem like they should be able to survive one-headed. If one head is sufficient to control their body when the other one sleeps, as we are told in their lore, then it seems like one head should be able to permanently control the body. In the question If one of an Ettin's heads dies, does the other head die?, Matt Vincent's answer points out that in first edition lore, an ettin explicitly could survive the loss of one head. Matt also compares the vorpal sword to a sword of sharpness, which cuts off limbs rather than decapitating. The sword of sharpness description explicitly says that if a creature has a limb removed, "the effect of such loss [is] determined by the DM", so why would that not also be true of a vorpal sword?

Zombies (and other mindless undead) don't seem like they need a head. They are not alive, just animated corpses. Their undead nature trait means they don't "require air, food, drink, or sleep." Their mindless soldiers trait means they are "unable to comprehend obstacles, tactics, or dangerous terrain." It's not clear to me why a thing that is already dead needs any particular part of its body. In the question Can a zombie survive headless?, the accepted answer (that they cannot) simply makes the exceptions-based argument; if the zombie didn't need its head, its description would tell us...but that seems like an unconvincing example for that particular creature.

In the question Vorpal Sword vs. Wildshape, multiple answers make use of the argument, 'no beast says that it can survive without its head, so no wild-shaped druid is capable of doing so'. And yet, a tour through the beasts reveals multiple creatures that, to me, appear quite plausibly capable of surviving decapitation. Some, because like the ettin they naturally have two heads (amphisbaena, two-headed crocodile, two-headed plesiosaurus) and others because they are fantastic versions of real-world creatures that regularly survive without heads (typically insects¹, thus giant fire beetle, giant fly, giant wasp, Pollenella the Honeybee)

Beyond the fact that "the description should tell us" excludes a large number of creatures that seem like reasonable candidates for surviving decapitation, there is the argument of equally applying the principle of "the description should tell us". That is, one of the conditions of immunity to instant death from a vorpal sword is if a creature does not have a head. Should the same principle apply? Should we assume that all creatures have heads unless their descriptions say otherwise? I can't immediately think of any creatures whose descriptions explicitly say they don't have heads, but I can certainly think of creatures that don't have heads (like the shrieker) where this is lack is not noted in the description.

Problems with 'The DM decides'
The description of the vorpal sword gives us one condition that will cause death ('can't survive without the lost head') and five conditions that will render it immune to this effect ('immune to slashing', 'doesn't have a head', 'doesn't need a head', 'has legendary actions', and the DM decides it is too big). Note that only one of these is called out as being up to DM adjudication. Two of them are known quantities described in stat blocks ('immune to slashing', 'has legendary actions'). If 'can't survive', "doesn't have', and 'doesn't need' were supposed to be adjudicated by the DM, why weren't those also included with the 'the DM decides' rules. Why were they grouped with things like 'immune to slashing' which is an objectively verifiable stat? Doesn't this imply 'the description will tell us' reasoning? If the DM was meant to decide this, the vorpal sword could easily have been written as:

The creature dies if The DM decides it can't survive without the lost head. A creature is immune to this effect if it is immune to slashing damage, doesn't have a head, has legendary actions, or the DM decides that the creature is too big for its head to be cut off with this weapon, or that it doesn't need a head.

Neither one of these arguments seems clearly a winner to me. The vorpal sword expects us to know which creatures don't need a head to survive. How are we expected to determine that?

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¹ While real-world insects do have a concentration of ganglia in their head section, these are mostly responsible for running just the head, and other ganglia clusters in other parts of the body run their own areas; it is a more dispersed arrangement than a mammal's central nervous system. Nor do insects have lungs connected to their mouth; they breathe through holes all over the surface of their body. So a headless insect will often survive for days or longer until they eventually die of dehydration or starvation.

Answer 1

The answer, my friend, blows in the manuals.

You already quoted the relevant rules & strategies to decide when a creature can survive without their head.

One can expect that mundane creatures (humans, dogs, birds, cats, deers, fishes) do not survive without their head. Notable exceptions are some insects, as noted in the question, but this requires some (basic) biology knowledge that a DM may lack, as I honestly admit in my case.

Fantasy creatures (elf, dwarfs, goblin, orcs, dragons, feys, zombies, ...) usually follows "classical" biology, so some actions such as beheading them kill them. Some particular fantasy creatures, ì(e.g., the hydra), have special rules (in this case inspired by Greek mythology).

Some others, like the quoted Ettin, does not provide any indication, or god-like creatures may be killed just by a lucky strike, as for using the Vorpal Sword on Vecna: and here comes the DM, the referee of the game.

As quoted in the question, DM's role is to describe the consequences of players' actions and build the world the characters are living in: when the rules and/or monsters' descriptions¹ are not clear, they have to make a call, adopt a ruling, stretch them for edges cases. This is exactly the spirit of the 5th edition, per Rule 3 quoted in the answer and per the very words of the Sage Advice Compendium:

The DM is key. Many unexpected things can happen in a D&D campaign, and no set of rules could reasonably account for every contingency. If the rules tried to do so, the game would become unplayable. An alternative would be for the rules to severely limit what characters can do, which would be counter to the open-endedness of D&D. The direction we chose for the current edition was to lay a foundation of rules that a DM could build on, and we embraced the DM’s role as the bridge between the things the rules address and the things they don’t.

There is no need to include in any creature stat block if the creature can survive without their head, since DND worlds/setting resemble real life biology. Putting a lot of rules, specifics, indications, interactions makes the game a Law Office job. Let me emphasize a passage of the SAC:

[...] no set of rules could reasonably account for every contingency. If the rules tried to do so, the game would become unplayable.

Anyway, I truly believe that some creatures with particular roles in adventures or campaigns (such as Vecna, for example) or creatures with multiple heads (e.g., Ettin) should include this information, due the interaction with powerful game features, such as the Vorpal Sword.

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¹ The case of the shrieker can be solved by reading the description and merging with real life knowledge: "A shrieker is a human-sized mushroom that emits a piercing screech to drive off creatures that disturb it". It is a mushroom, hence it has not an head. This is nonetheless a DM's call.