Medievalism depends greatly on two cycles of chivalric legends - the Arthurian and the Carolingian. These were the main source material for Medieval Anglo-French troubadors, and as a result ended up infused with love stories.
This is something you won't find in other sources. Neither Biblical nor Graeco-Roman legends have alluring love stories. The few women they have - Delilah, Jezabel, Salome, Helen, etc. - are awful persons.
But the Arthurian and Carolingian cycles are chock full of romantic material.
First of all, no need to lump Roman stories with the older Greek ones. Virgil for example isn't Homer's pupil so his view on the Homer tales is something completely different.
Stories such as Dido and others of course may be lumped into a 'Greco-Roman' context, but not all of them.
And how is Helen an awful person? She's barely even mentioned, there's not even a description of her (for some odd reason she's depicted as a blonde but Homer leaves her undescribed because she's left to the imagination of the reader/listener to have a description of "the most beautiful woman") other than her love for Paris and her regret for abandoning her husband which she later reunites with upon Paris' death.
Then we have to define what 'alluring' means? Alluring to whom? Because that's rather subjective, no?
The Greeks also have the story of Orpheas, who is quite possibly the most romantic tale of them all with Euridiki. Pure love, no wars and bloodshed for a love of a woman.
An even more ancient tale was Eros (Love) and Psyche (Soul), which imo should be considered the greatest love story of all time but it's not even half known around the world. It's very underrated and lesser known in Greece too.
Another epic one is Jason and Medea. Perseas and Andromeda is a symbolic one.
Another would be Leandros and Ero, which I think was also highly rated by the Romans.
There are also other rather weird ones, but they fall into this 'magical' realm. Alfios and Arethousa for example. End of the story is something like she became a fountain and he couldn't bear away from her so he became a river that connects with her etc.
And there's possibly several other 'big' ones at some point or more regional ones that got lost in time.
I think the biggest difference in the ones you mentioned is their randomness. As you say, they are 'safely obscure'. They have no geographical context and no historical context. Whereas in the Greek ones (and the Roman ones later on), they are more literal in the sense that they want to show attachment to something. Be it a historical situation, a real life person that lived, a heroic tale (see Heracles and Dionysus), a religious/mythological affair and so on.
So essentially you are describing the birth of popular novel literature as we know it. We have evidence of ancient novels, but we do not know of them as some sort of epic literature that influenced people and had its popularity survive through time. I'm not even sure how many romantic novels still exist in Greek or Latin from antiquity, but it's not something you stumble upon.
But for many the legend of Arthur is something like early English mythology, the death of ancient Britain and the birth of England and so on. It also has this mythological allure, it's not just a fiction novel and it's not even a novel as you could find a bunch of variable versions. Though I'm guessing that by Arthurian legends you are referring to legends that were referring to this period of time more than the actual Arthur legend of course.
So back to the question.
Why always a dragon? Christianity? Or were dragons popular in the folklore of that region for centuries?
I'm not agreeing that the Medieval era has much to do with 'romantic love' as I think it has more to do with the closeness of origin in terms of the timeline. It was the closest 'previous era' available and it was rather undocumented so it was easy to create random stories and people probably wanted more of that. And they were also situated in proximity of those who had written them. How many stories from then were written about people in India, Persia, Eurasia, Greece or Africa? My guess would be zero and if I were betting I'd say it's definitely less than 5 in total.