Ah, but we HAVE had real dragons! Dinosaurs!
I'm being flippant, but it's likely the case that the widespread dragon legends likely have do with the fact that dinosaur bones can be found pretty much all over the world.
In regards to kujoestars's remark that all irl creatures that reproduce asexually also reproduce sexually, consider that FFXIV dragons are VERY unlike irl creatures. Irl creatures need sexual reproduciton in order to mutate and evolve over generations - but FFXIV dragons mutate and evolve within their own (considerably long) individual lifespans. This could well negate the evolutionary advantage that sexual reproduction brings to the table.
It's worth noting, though, that in spite of this, dragons for some reason choose to be gendered, and choose to pair off into mated pairs (such as Tiamat and Bahamut). Whether these mated pairs actually do reproduce sexually, or only do it for companionship is unknown.