That premise always makes me think the popular 'Harry raises a dragon' fics often skip over the logistics. A dragon isn't a slightly large owl. It fundamentally alters the conflict with the Dursleys from the start—they can't exactly lock a creature that breathes fire in the cupboard under the stairs. It would force an earlier, more violent break from Privet Drive, maybe even have magical authorities intervene before Hogwarts. The dynamic changes because Harry’s primary relationship becomes with this dangerous, magical creature, not the wizarding world. He might even become more isolated, distrustful of people, seeing the dragon as his only real family. I’ve read a few where this leads him down a darker, more independent path, less invested in the 'saving the world' plot and more in protecting his bond. The political fallout alone would be huge—imagine Fudge’s reaction to 'The-Boy-Who-Lived-and-His-Pet-WMD.'
Honestly, most stories that go this route end up making the dragon a plot device for power escalation, which gets boring. The more interesting angle is the psychological shift: how does being responsible for something so destructive, yet fiercely loyal, shape an eleven-year-old's morality? Does he become more possessive, more feral? It's a cooler character study than just giving him a new weapon.