I'm not sure they are actually so ubiquitous. Nor do I see those creatures that are often clumsily grouped under the same English word as related - either genetically or be nature of their characteristics. Asian dragons, which can be rather wolfish in appearance, are often regarded in fairly positive terms. The Germanic giant worms, for which we use the Latin-based English word "dragons," were ground hugging, dangerous, and rather snake like.

Giant monsters are common internationally, but it is wrong to allow the application of the term "dragon" to various entities to imply that those entities are similar or related. They are not necessarily similar and they are certainly not all related.

Many cultures have folklore about human-like giants - and at least these creatures share a lot of similarities - but we would not look for them to be a result of widespread diffusion. The cultural/historical process of populating the world with certain supernatural creatures finds itself hemmed it by the common human experience, so some of the outcome seems similar in some ways even when it is not related.

You might be interested in a lecture by J.R.R. Tolkien on Beowulf where he repeatedly touches on the role of the dragon. He suggests that the narrative value of the dragon is that of a great foe who can serve as a fitting challenge or end attesting to the greatness of the hero. Tolkien says that "for the universal significance which is given to the fortunes of its hero it is an enhancement and not a detraction, in fact it is necessary, that his final foe should be not some Swedish prince, or treacherous friend, but a dragon: a thing made by imagination for just such a purpose."

We might suppose from this argument that storytellers latched onto dragons because great heroes need great adversaries.