Breasts on the sphinx go back, in terms of classical representation, to at least the
16th century, so there's some precedent for that. (Of course, D&D uses history and mythology for exactly as much as its convenient, but still it's not like this idea was pulled out of thin air.)
With regards to the larger point about "realism" in fantasy, I feel that there are two points that need to be made (and others have done so already; I just want to underline them):
First, "realism" is not the same thing as "internal logic and consistency in the game world" (though it's often used as a shorthand for it).
Second, I'm of the opinion that fantasy game worlds use a presumption of "functions as per the real world unless told otherwise." So we'd assume that a female non-mammalian creature doesn't have breasts unless we're given evidence to the contrary. Since we're given evidence to the contrary in the case of female dragonborn, then we move on to the corollary of the above rule - "when told otherwise, the fantastic overrides the realistic, with no regard for real-world 'natural' laws."
So in other words, I don't find it "unrealistic" that female dragonborn have boobs - simply put, the basic conceits of a fantasty game (particularly one with prevalent, powerful magic and interventionist deities) mean that anything is up for being changed from our real-world expectations, and in this case the game has exercised that inherent option. (That's not even mentioning that we have
egg-laying mammals that nurse their young in the real world anyway, so this is hardly a stretch of the imagination.)