The answer to this is more complex than you might think - isn't that always the way!

First, the folk belief about dragons and giants generally involved the idea that these creatures were remote - either existing in a distant place or in a remote time. Pre-modern folk did not tell stories about people actually encountering dragons and giants. They might hear reports of people seeing a dragon in the clouds, but these were generally conveyed as third-hand reports.

Folklorists make a distinction that separates first-hand legends (called memorates) from legends that people told and retold. Even today, people tell memorates about times when they say or sensed a ghost; they may have also heard or even retold the urban legend of the Ghostly Hitchhiker: both contain the same belief in ghosts, but in the case of this supernatural being, it can figure in first hand as well as third-hand legends. In the case of giants and legends, one did not normally encounter memorates; rather, legends about giants and dragons were told and retold, and the location or time was remote. For a long time, for examples, the English felt that Wales and Cornwall were natural homes to giants, but no Englishman would expect seeing one rampage in his local village.

As the world became a smaller place with modernism, it was easy for these remote entities to fade from the belief system as remote places became better known, and one can probably "chalk all this up" to changes that were occurring with modernity in the nineteenth century.

At the same time, we have to understand that the European folk told stories to be believed (legends) and stories that were understood to be fiction: the folktale (often called "fairy tales") were the novels of the folk. While the folk might have seen their belief in dragons, giants - or anything else - decline, that doesn't mean that these entities did not continue to figure into their folktales. And the fact that these creatures took a part in the folktale should not be taken as a matter of belief: millions are watching the final episodes of Game of Thrones, but that does not mean that all of those people believe in dragons, giants, and/or white walkers.

Fairies represent a more difficult subject to tackle. Borrowing from my recent book, The Folklore of Cornwall: The Oral Tradition of a Celtic Nation (2018):

There is evidence that people have always thought their beliefs in the supernatural were fading and that earlier generations were more fervent in their fairy faith. Asserting that a belief in these entities was a bygone facet of English heritage features in Chaucer’s fourteenth-century introduction to ‘The Wife of Bath’s Tale’, which the character sets ‘In the olden days of King Arthur [when] … all this land was filled with faerie’. The Wife of Bath adds, ‘This was the old belief’. It is a theme that appears to have resonated over the centuries with a repeated assertion that people regarded those from previous centuries to have possessed a stronger faith in the existence of a fairy world. Writing in 1997, Linda-May Ballard cites Jeremiah Curtin as describing the idea of a waning belief in the fairies in his 1895 publication on Irish folklore. Ballard then poses the question, ‘Might it be that the idea that fairy belief is fading and belongs to the past, is part’ of the wider tradition embracing the belief in these supernatural beings?

... Seeing Fairies: From the Lost Archives of the Fairy Investigation Society, Authentic Reports of Fairies in Modern Times, provides evidence of British tradition enduring into at least the mid-twentieth century. Modernism affected but did not extinguish fairy traditions. A Cornish example from 2017 reinforces the idea that while folklore may change, aspects of belief can defy intuition by lingering over time. The Packet, a newspaper serving Falmouth and Penryn in Cornwall, reported the one-hundredth birthday of Falmouth native Molly Tidmarsh. The centenarian implied that some of her good fortune in living so long may have been due to her birth under a ‘piskie ball’, a round lump of clay, fired together with one of the tiles used on the roof ridgeline of her family’s home and business. Molly suggested that these objects were created to distract piskies who sought to come down the chimney to cause mischief for the occupants of the house. Instead, the piskie ball would entrance them, and they would dance around it until dawn, at which point they would disappear. It is unclear, and largely unimportant, if Molly Tidmarsh believed good luck was hers because she was born under the ball; what matters here is that piskies featured in a newspaper article in 2017 without a need to explain what they were. Molly remembered a tradition of the early twentieth century and it still resonated with readers one hundred years later.

So what are we to make of all of this? It appears that it may be a long-standing characteristic of folk belief to regard previous generations as more superstition than "my generation" and that this has been true for generations. It also appears that belief in fairies has thrived - and is thriving - more than we might know or appreciate.

Fairies, like ghosts, figured into memorates - the first-hand accounts - and they still do in various ways. I'm not sure we can say that they have "dwindled to the point of being considered completely nonsensical or simply superstitious" - any more than Chaucer's generation viewed this same question: "we" are too sophisticated to believe, but "previous generations" were silly in that regard; future generations may regard us in the same way - indeed, it seems likely that this will be the case.

Fairies were known to leave circles in fields because of their dancing, to appear in the night as glowing lights, and to be interested in capturing people. We may regard all of that as superstitious nonsense, but all of that is a short step to aliens in glimmering UFOs during the night doing much the same. So, is sophistication when it comes to belief that much a hallmark of modernity?

Sources from my book: John H. Fisher, editor, The Complete Poetry and Prose of Geoffrey Chaucer (New York: Holt, Rinehardt and Winston, 1977), p. 120; Linda-May Ballard, ‘Fairies and the Supernatural on Reachrai’, in Narváez, The Good People, p. 91; note 9; and see Young, ‘Five Notes on Nineteenth-Century Cornish Changelings’, p. 67; Marjorie T. Johnson, Seeing Fairies: From the Lost Archives of the Fairy Investigation Society, Authentic Reports of Fairies in Modern Times (San Antonio, Texas: Anomalist Books, 2014); The Packet, 22 August 2017.