The suspension of disbelief is often helped by the small details that fit in with our notions of reality. I don't have to hand wave everything because I've hand waved one thing. I am coming to really hate the argument "If you can accept this fantastic thing, you should be able to accept that one too."
I'd generally agree, but there's a playability threshold for any of this. "I have to play a character with an alien anatomy" is a pretty high playability threshold.
But I get it, an argument from the meta-game isn't going to convince anyone who gets hung up on the fiction of it. So I could also put it this way for the "logic!" crowd:
Dragonborn are, in 5e myth, "shaped by draconic gods or the dragons themselves." They hatched fully-formed from dragon eggs as divinely created magical beings.
Also, they have genders and apparently breed true (first words in the dragonborn entry in the PHB:
Her. Father.).
They didn't evolve. They didn't arise from lizards or dragons or dinosaurs or what-have-you. They were artificially created. The same is actually true in 4e lore of minotaurs and shardminds -- created, artificial beings.
This changes the convo from: "gems don't have boobs" to "Why would gem creatures choose to have a gender identity shared with other humanoids?" or "Why would dragon-gods give their creations mammaries?"
That's a question you answer mythically. Like, maybe shardminds take a "Hedwig" approach to gender: they were originally all one creature, and their different gender identities are things that they regard as flaws, signs of a fallen people, broken in half. This fits the myth of their creation, as bits of a shattered gate. A shardmind adopts the form and identity of a human female (or feels like this is the natural expression of her form) because she sees in that division an acknowledgement of a great tragedy, a division where none need exist.
For dragonborn, the idea behind mammaries might be some of the same benefits real humans get from them: close family bonds and strong ties between mothers and children. The idea of dragonborn clans reinforces this -- heck, maybe dragonborn clans are matrilineal? -- by emphasizing family relationships. If you wanted your artificial race to have strong family ties to each other, functional breasts are a good way to do that.
For minotaurs, if you're making a creature bipedal and making them mammalian, udders don't make much biological sense. Upright postures drive mammaries to be carried higher, and don't produce the racks of six or eight that we see in the quadruped world.
In-universe, it's perfectly sensible.
And if you want to talk about why it must be that way in-universe, we're back in the meta-game, and "because a lot of people like to play characters that are anatomically relatable" pops up. I mean, why do elves and dwarves have breasts, if you really want to press it.