Through no fault of your own, there's a bit of wrong approach to assumptions embedded in your question. Some of this smacks of Euhemerism, which takes its name from Euhemerus, a Greek writer of the late 4th century BC. He suggested that oral narratives - the myths of his time - were based on real people or inspired by real things. Every since then, there have been attempts to "chase down" the origin of folk narrative and belief, attempting to find the source in real things. Folklorists generally see this as the wrong way to approach things - but it doesn't inhibit people from trying, and it inspires several questions on this sub every week!

To provide an example close to what you're after here: people have long questioned why some people suddenly die, and there is particular concern about infants who either die suddenly are who after a point seem to fail to thrive. It was easy to imagine that there was some supernatural agency at play here, but it did not cause people to create an entity that was responsible for that supernatural event. Instead, they looked to what they "knew" existed in their surrounding and the process went something like this: there are elves all around us, sometimes invisible, and always lurking about in one form or another; they are attracted to the company of people and if care is not taken, they will abduct people; that person died suddenly, or that infant seems to be acting strangely, therefore, the elves (which we know to exist) must have acted and likely abducted the person (or infant), replacing it with a changeling that appears as the person's corpse (or as a failing infant).

The folk did not create the idea of elves to suit the circumstance. They explained the circumstance with the elves because they seemed to be the likely culprit.

An unusual event does not "trigger the creation of certain creatures"; rather, it causes people to look at the spectrum of beliefs that they have to explain what just happened. An event can put wind in the sail of a belief, but under normal circumstances it does not cause the belief ("under normal circumstances" is put here to allow for the exception, because with humanity, anything is possible!).

Monstrous creatures can serve to deal with fears: I fear my infant son won't thrive; he may not thrive because elves may abduct him (they prefer baby boys); I will place iron over the crib to prevent the abduction (they hate iron) and I will dress my baby boy as girl to make the elves less interested; my fear is consequently reduced because I have taken active steps to address the source of my fears. Here we see reality, real fears, and beliefs all entwined in action and the easing of fears, but there isn't a causal relationship in that the fear did not create the belief in the entity.

As described elsewhere today, people feared that the elves were interested in stealing the essence of a harvest, and so, again, there was a ritual that served to reduce community anxiety. It was also a time to enjoy the moment and celebrate the end of the exhausting harvest. As is always the case with farming, the crop ripens even as the weather starts closing in. Farming is a risky business, and there is always the danger that the harvest will fail and starvation threatens, so celebrating a good harvest - and magically protecting the results - was in part a practice of magic and in part just good fun that reinforced community bonds.

Here is an excerpt from my recent The Folklore of Cornwall (2018) that addresses at least one harvest ritual and how it may be understood:

Hunt, Courtney, Jenkin and others document a ritual known as ‘Crying the Neck’. As noted, Rowse also mentions it. The practice celebrated the end of the harvest using a phrase of unclear origin and meaning. Sources describe the ceremony in various ways. In one case, a reaper cut and plaited the last stalks and raised them up, while workers gathered into three groups. The first shouted three times, ‘We have it’. The next answered three times, ‘What ’av ’ee?’. The third replied, again three times, ‘A neck!’. This was answered by all with a cheer. Sometimes everyone stood in a circle with the person holding the neck in the centre. Hunt describes the group starting the chant with ‘The neck’ followed by ‘We yen!’ which he translates as ‘we have ended’. Thomas disputes this translation and suggests, instead, that the meaning is ‘We hae ’im!’. The plaited stalks hung with honour on a wall, often near the hearth of the farmhouse.

Some sources mention a second phase of the ceremony involving a young man who raced with the neck to the farmhouse. There, a female servant stood guard with a bucket of water, and if the man managed to enter the house without being drenched, he could steal a kiss from the woman who had failed at her task. ‘Crying the Neck’ nearly died out in the twentieth century, presumably in part because mechanized harvesting reduced the workforce and changed the dynamics of the process. Nevertheless, the tradition enjoyed a revival thanks to the Old Cornwall Society. The term ‘Crying the Neck’ also appears in Devon and South Wales and it is clearly part of a larger tradition that used other phrases elsewhere in the British Isles for similar rituals.

The pioneering Scottish anthropologist James Frazer (1854–1941) incorporates the practice of ‘Crying the Neck’ and its other British counterparts into a larger discussion about a figure he calls ‘the corn mother’. For Frazer, these practices echo imagined Neolithic rituals that involved sacrifices to ensure the bounty of the harvest. Thomas subsequently takes up the motif in his treatment of Cornish folklore, embracing Frazer’s conclusion that the folk memory of ancient sacrifices surfaced in recorded Cornish folkways.

Jacqueline Simpson and Steve Roud in A Dictionary of English Folklore cite the existence of numerous harvest effigies from various places in Britain, and they provide an eloquent critique of Frazer. They point out how attempts to understand these sorts of harvest ceremonies have been ‘stultified by the tacit acceptance of J. G. Frazer’s theories’. In addition, they describe how the failure to reconsider this folk practice is overdue since ‘Frazer’s ideas have long been discredited’. In a call to action, Simpson and Roud conclude that ‘we still need to move on to a post-Frazer era’. This raises the question then as to what can now be said about the practice of ‘Crying the Neck’ in south-west Britain.

Pre-industrial northern European farmers typically believed that the vitality of the whole crop remained in the field until the final stalk had been cut and workers had corralled the strength of all the grain into the last corner. Legends from Scandinavia, for example, speak of the risk presented by this concentration of the harvest’s potency. Stories told of witches and supernatural beings trying to steal the last grain, because with it, they could take everything that was good about the entire field, leaving the farmer with a crop that would fail to provide nourishment. In those places where farmers believed this was a threat, they often adopted rituals that would protect the last stalks, even though this quantity was insignificant compared with the entire harvest.

The Cornish practice of ‘Crying the Neck’ fits into wider regional practices of magically safeguarding the harvest’s essence from theft at the critical moment. The tradition is at once consistent with what occurred elsewhere while also being unique in its own specific details. Examining this custom as part of wider traditions provides a means of understanding Cornish folklore as something that occupies a place within the greater region but which at the same time remains distinct. By the time the ‘Crying the Neck’ ceremony was recorded, most participants probably did not know about any deeper meaning in the event. It was merely a common, age-old practice. Folklorists sometimes refer to this sort of holdover as a blind motif; that is, people retain a custom but have forgotten its significance. Suggesting what it meant based on contemporary or near-contemporary observations from elsewhere is problematic in its own way, but it is less extravagant than inventing a Neolithic explanation, reaching back thousands of years into the past with nothing more than speculation, as Frazer had done.

Perhaps that creates more questions than it answers. Free free to let me know all the ways I have failed to answer your question!

Short answer:

It isn't likely that anyone intentionally created stories of monsters for a self consciously practical reason. That's the kind of thing you find in the movies today (eg The Village). These were stories people liked hearing, and they were repeated and elaborated, with useful or psychologically satisfying messages, but they weren't Public Service Announcements. It's the nature of folklore that it evolves through repetition by many over time, rather than having a single invention event and author.

Discussion:

Folklore is more the domain of anthropologists than historians, particularly as you're interested in a "cross section of human culture". Anthropologists are the folks who study human nature, and when you're asking "what did people think" but not asking about any particular time or place . . . that's an anthropology question. We don't have records of people deciding what stories to tell, for what reason. Its anthropologists who study human nature and behavior, and how those aspects of human life develop into a culture. They're also more practiced with oral traditions than are historians.

In terms of history, we can say that the interest in monsters is widespread, and leaves a historical record. We find monsters in the earliest recorded literature, works like the epic of Gilgamesh, with its monstrous Enkidu, a sort of bull-man. Reaching back to some of the oldest oral traditions, the Australian Aborigines have stories of Bunyips and Yowies . . . you'd be hard pressed to find a culture that doesn't have its monster stories. They don't typically have some explicit practical reason-- beyond perhaps "kids, don't play around water without a grownup"; Japanese parents will warn of the Kappa in this way. For an Australian, a story of a Bunyip might have served a salutary purpose (not getting eaten by crocodiles)-- but there's no evidence that it was intentionally invented for such a reason.

Speaking of reasons to steer clear of the water, looking at Anglo-Saxon charters, we find more than a few "Grendels mere" (eg "lake of Grendel", as in Beowulf. And having evoked Beowulf, we should also mention J.R.R Tolkien. He was a scholar, likely better known to you for Lord of the Rings: he makes the observation that while we have a very firm line between "Gods" and "Monsters' -- for earlier men this line was much fuzzier, often they're related or allied, as in the case of Polyphemus the giant cannibal, who is also the son of Neptune.

As an historical matter, we can look to St. Augustine. He has examples of monsters as being both stories devised by men, and real things created by God to show his power. He discusses this issue and the meaning of the word "monster" -- derived from the Latin monstrare (="to show") because they signify something and demonstrate the power of God over nature:

As therefore it was not impossible to God to create such natures as He pleased, so it is not impossible to Him to change these natures of His own creation into whatever He pleases, and thus spread abroad a multitude of those marvels which are called monsters, portents, prodigies, phenomena, and which if I were minded to cite and record, what end would there be to this work?  They say that they are called “monsters,” because they demonstrate or signify something; “portents,” because they portend something; and so forth. . . [the existence of these demonstrates] that God will bring to pass what He has foretold regarding the bodies of men, no difficulty preventing Him, no law of nature prescribing to Him His limit.

He also suggests that men invented these stories ("What Fables Were Invented at the Time When Judges Began to Rule the Hebrews.") -- but he doesn't actually have any historical evidence for this. He views these man created myths and monsters with some bemusement, not understanding how they could tolerate the treatment of Gods with such indignity.

The nearest I can come to a "monster story created for a reason" might be the story of the Golem of Prague, a story of a creature created to defend Jews against anti-semitic violence. Although the story purports to be that of a 17th century rabbi, so far as we can tell its a 19th century invention, a sort of superhero. The notion of a golem had existed before this story, but it doesn't take on its monstrous form until these 19th century works.

What we know from history is that there are lots of stories of monsters and demons that _answer_ some fear. The ancient Mesopotamians, for example, had fears of evil spirits and demons. We've got records of their exorcisms and protective amulets. For them, a spirit or a demon was an answer to something unknowable -- "why am I sick", "why did the crops fail", "why can't I get pregnant". So human need made some stories popular, but there's little evidence of them being purposely invented for any reason.

Sources:

John Block Friedman, "The Monstrous Races in Medieval Art and Thought" (Syracuse University Press, 2000)

J. R. R. Tolkien, "Beowulf: The Monsters and the Critics," Proceedings of the British Academy 22 (1936): 245-9

Rudolph Wittkower, "Marvels of the East: A Study in the History of Monsters," Journal of the Warburg and Courtauld Institutes 5 (1942): 159-97

Holden, Robert (2001), Bunyips: Australia's folklore of fear, National Library of Australia

Frankfurter, David. “Scorpion/Demon: On the Origin of the Mesopotamian Apotropaic Bowl.” Journal of Near Eastern Studies, vol. 74, no. 1, 2015, pp. 9–18.