So introducing a dragonborn could potentially change the entire dynamic of the campaign and I find it perfectly understandable if a DM doesn't want to deal with that, or put in another way, would not have fun dealing with it. And I also understand that a DM could hand-wave it and just have everyone react to the dragonborn just lika any other PC, but that could put a strain on the feeling of verisimilitude of the DM and the other players. And there are of course other ways of handling it, not all DMs or games are the same or have to be the same. My fun is not everone's fun
I can also see a fabulous campaign where all this happens, but from another perspective as a DM I'd be loathe to let one single player have that amount of spotlight at the detriment of the other players, unless they are all comfortable with the dragonborn being the center of attention and a driver of how the campaign develops. Maybe everyone plays a dragonborn?
Also, the above example presupposes that exotic races (e.g. dragonborn, tieflings, owlin, loxodon, aaracokra, tortle) are rare. If the Mos Eisley cantina is default in a setting, a dragonborn wouldn't even register as being out of the ordinary, but I'd wager a guess that several DMs who are limiting e.g. dragonborn aren't big on other exotic races being part of the campaign either.