I don't really think that Dragons are really that important in FE. Their inclusion in many games seems incredibly vestigial at times, having no place in a the narrative. An animalistic beast or demon has no real place in a game where the conflict is mostly between humans and their respective causes. Take the Fire Dragon, for example. FE7 doesn't exactly have masterclass villains, but the Four Fangs at the very least feel like people with their own values and lives to live. The Fire Dragon really only exists as a random obstacle for the player to fight because "The final boss has to be big!". It has very little presence in the story and doesn't have a character by nature of being a crazy beastie. Not only that, but the times that FE does have a good Dragon character, they're basically cheating because they are mostly portrayed similar to humans who can simply transform into dragons to fight. I love characters like Dheginsea and Tiki, but they're really just guys who can turn into Dragon in terms of the narrative.
So Dragons are kinda dumb, I guess.