From a biological standpoint, reptiles with breasts makes little sense, especially since dragonborn are hatched from eggs - they have no need for feeding young, therefore they would not be a good signal of fertility (and therefore serve no purpose.
From an art standpoint, I can see it purely to designate female from male dragonborn to the viewer. Visual cues of female features (long hair, slimmer build, softer features) let us know which is male and which is female. Since dragonborn don't really have many obvious markers, breasts make sense to be an easy visual identifier.
As a furry I am totally cool with reptile boobs, but the dragonborn design isn't exactly aesthetically attractive so it's moot.
From an art standpoint, I can see it purely to designate female from male dragonborn to the viewer. Visual cues of female features (long hair, slimmer build, softer features) let us know which is male and which is female. Since dragonborn don't really have many obvious markers, breasts make sense to be an easy visual identifier.
As a furry I am totally cool with reptile boobs, but the dragonborn design isn't exactly aesthetically attractive so it's moot.