A key component of world-building is not just what types of fantasy creatures should be included, but how to find the connections between them, the environment, humans, religion, and geopolitical entities such as kingdoms, empires, city-states, and tribes. Creatures such as dragons, griffins, and mammoths can change warfare, migrations, human survival, and the very ecology itself.
The Targaryen dynasty especially proved this point, by escaping the destruction of Valyria and settling in Westeros. Though they did more than setting up their own little nation on Dragonstone Island, rather they conquered the entire continent of Westeros and subjugated entire kingdoms, all through the use of dragons as instruments of war. This can only be possible in regions like pre-Targaryen Westeros when there was no presence of dragons or any other form of the animal capable of fighting against such creatures because it would mean that there would be no defense against conquest by the dragon-riding invaders.
A foreign invading group would bring disasters foreign to the native population. This parallels the use of guns and diseases brought by Europeans when conquering the rest of the world. In the case of the Americas, the indigenous population was not immune from smallpox until the Europeans brought it, which indirectly decimated them.
If foreign agents like diseases can cause this type of damage to entire populations in the real world, then foreign creatures, such as dragons, can prove to be apocalyptically destructive in the fantasy world. A notable example of a dragon that fits that description is Smaug from "The Hobbit" who conquers an entire castle of dwarves and converts it into a lair surrounded by a hoard of gold. This is when fantasy creatures cannot be tamed and become a destructive force.
When these creatures are tamed, they retain a symbiotic relationship with their human captors that transcend use as weapons. In the case of Victor Milan's "Dinosaur Knights," (which is a fantasy novel that replaces dragons with dinosaurs) the hides of dinosaurs are made into protective armor, which would make sense considering how dinosaurs are also used as instruments of war and the only rough surface that can protect the owner from a war-hadrosaur's bite is the skin of a dinosaur who's skin is already adapted enough to withstand bites and scratches.
The uses for attack and defense would ensure that there is a cycle of dependency between humans and dragons. Of course, the use of dragons would go beyond being used in warfare. If these types of creatures have the ability to be domesticated and rode by humans, fly at great distances, and breathe fire, then the possibilities of traveling the world would be quite literally boundless. This is especially true when Jaenara Balaerys, a Ghiscari dragon-rider, explored all of Sothoryos, one of the continents of the "Song of Ice and Fire" series.
Can you imagine that level of exploration becoming more commonplace as more creatures are introduced? This would be where readers would find a more clandestine and complex system of warfare which consists of entire theaters of war consisting of dragons. While there would be ground warfare with armies of cavalry and phalanxes, there would also concurrently be dragon-riders from above.
Even though fantasy creatures do not exist in real life, it can be argued that the very image of them was enough to change human interaction with nature, by inspiring superstitions, mythologies, and sigils on coats-of-arms. The inspirations for dragons also existed within the real-world, specifically by theories that dragon myths came from ancient observations of dinosaur fossils, which lead to the speculations of a race of dragons (and what leads Milan to include dinosaurs in his fantasy series).
Of course, this opens up Pandora's box, but all of the world's evils do not pop out, but the creatures from every mythology around the world. Not to be too political, but a lot of the most popular fantasy works consist of mythological creatures from European interpretations, such as dragons, dwarves, elves, etc. If European dragons can exist in a fictional world, who is to say that Chinese dragons cannot also exist in this world? If multiple mythologies can exist in one cosmopolitan mythopoeia than the possibilities would be endless when it comes to migration patterns and cross-breeding.
What if dragons become an invasive species, by outcompeting all the other animal life and out-consuming all of their prey and plant life? If one were to apply eco-literary theory to dragons in mythology, it can be argued that they would be catastrophic to humans and the environment. Perhaps the human civilizations would focus less on their own squabbles and more towards that scaly threat to their crops and livestock.
However destructive dragons are to everything living and nonliving, it is definitely obvious that these creatures define the animalistic power within fantasy. Dragons do more than provide the fantasy label, rather they dramatically reshape the connection humans have to the biosphere in their world. The existence of dragons plunges the reader into a world of epic uncertainty, leaving behind the doldrums of daily life and into the world where humans and creatures that represent the former's power can exist.