The Spectator has the Create Food and Water action (Monster Manual, p. 31):

Create Food and Water. The spectator magically creates enough food and water to sustain itself for 24 hours.

I don't understand why the Spectator must to use an action in order to create its own food and water to sustain itself.

Wouldn't be easier to add something like the banshee's Undead Nature trait?

Undead Nature. A banshee doesn't require air, food, drink, or sleep.

They could have made something like:

Spectator Nature. A spectator doesn't require food or drink.

Is there any important mechanical difference between both abilities? I mean, any exploit, advantage or drawback that has create food and water over it doesn't need food nor water.

Because that's how it was in previous editions of the game.

In AD&D book Monster Manual II (1983) by Gary Gygax, the ability to create food and water is one of the spectator's four eyestalks, the others being cause serious wounds, paralyzation ray, and telepathy.

The special quality of "Undead Traits" didn't really exist until D&D 3e (2000), which took design influence from Magic: the Gathering to apply general traits to specific monster types. The fact that undead don't need to eat or sleep wasn't really considered relevant by the designers of the very early editions of the game, when D&D was largely about fighting monsters in dungeons rather than any kind of realism.

In the D&D third edition book Magic of Faerûn (2001), the spectator similarly has the ability to create food and water with one of its eyestalks. Its other three were inflict serious wounds, hold monster, and suggestion. An updated version of the creature in Lords of Madness (2005) changes the creature so it creates food and drink as an innate ability, and one of its eye stalks instead causes fatigue.

It needs to eat and drink because according to its lore, the spectator is dedicated to to guard a specific place or thing without the luxury of leaving to hunt for food. Beholders are traditionally a type of living creature known as an Aberration, and therefore it would not be correct to simply make them Undead. Aberrations frequently have to eat, and the large mouth of beholder-like creatures strongly suggests that it is a creature which must eat to survive, and perhaps even greatly enjoys eating. It's therefore highly thematically appropriate for the spectator to be able to create food.

Giving creatures the ability to cast a single spell is a long-standing D&D mechanical tradition that dates back to the earliest editions of the game, when the easiest way for designers to give a monster a magical capability was simply to allow it to cast a spell normally available to a player character spellcasting class such as the cleric. D&D third edition often did this, where they were generally known as spell-like abilities.

It's not unthinkable for living creatures to be immune to the need to eat and drink, of course. The elan are a race of people who are of Aberration type, and they can sustain themselves without food or drink.

Because monster quirks bring them to life

There is indeed an important mechanical difference between a Spectator and the banshee you chose as your example: Aberrations are not dead. The Death Tyrant, you will notice, has the Undead type and not the Aberration type. On the other hand, Mind flayers are Aberrations too, and it is their choice of diet that defines them as a staple of D&D. The need for food and drink of the Spectator is not quite as vital as all that, but it's still part of its flavour.

Frankly, the ability to create food and water is not the most 'complex' trait of the Spectator, from a DM's point of view; its madness is, if you want to bring it forth well. First of all you need to determine what form this madness takes (the Madness tables in the Dungeon Master's Guide will certainly help), and then you need to think about how it affects the Spectator's reactions and decision-making.

But little, or big, details like this help make monsters feel unique. If every guardian monster didn't need to eat or drink, they might as well all be golems. The Monster Manual is there to give you inspiration.

You are, of course, always free to modify any monster however you see fit for your campaign. And even if you and your players simply cannot come up with ways to play such a quirk out, you can safely ignore them, nothing bad will happen. But imagine a Spectator refusing gold, but letting itself be bribed by a delicious and moist cake, because decades of eating bland created food make it unable to resist the temptation? That could become a scene to remember.

A spectator is living.

The creature feature that allows a monster to function without food or drink is generally reserved for Undead, Constructs or Elemental creature types.

Undead Creature Types

Crawling Claw, Mummy, Skeleton and Bone Naga are some examples of undead creature types from the MM that require no food or drink (or air or sleep). Even Zombies in D&D 5e require no food or drink - no brains for D&D zombies.

Death Knights are the only undead in the monster manual that do not have this feature. They apparently require food and water. Will-O'-Wisps do not need drink, sleep or air, but they do feed on fear.

Construct Creature Types

Constructs are made not born (MM 6) and often do not require food or drink (or air or sleep). Golems, Animated Objects, Scarecrow and Shield Guardians are some creatures of the Construct creature type from the MM that do not require food or drink.

Homunculus and Modrons are the only two constructs in the MM that do not have this feature. They do require food and drink.

Elemental Creature Types

Elemental creature types also generally do not need food or drink. This includes Elementals, Water Weird, Mephits and Azers and others in the MM.

Genies, Salamanders and Xorn are the only Elemental creature type that do not have this feature.

Other than powerful immortal beings, like Angels there are no other creatures that can survive without food and drink.

What about the Spectator?

A Spectator probably doesn't have this creature feature because it doesn't fit in with the general standards established in the MM for creatures with this feature. It's partially an issue of narrative, and partially an issue of consistency.

A Spectator is not of the Undead, Elemental, or Construct type. They are just badass and can conjure themselves all the food they need. This is probably necessary because they have to hang around one spot for 101 years guarding some treasure they've been summoned to protect.