Y'know, I just realized how Dawn of Justice could have been a good title.
Superheroes are metaphor made text. When someone is overcome by their rage, one might say they become a monster; the Incredible Hulk literally becomes a monster when he gets angry. Given that level of heavy-handed symbolism, a title that doesn't carry at least two meanings is just not trying. A great example of a good superhero title is Superman: Red Son, which manages to pack at least three meanings into just two words.
So let's think about our characters. Batman is the Dark Knight because, while he operates with a ruthlessness that concerns some people, he still has his own code of honor. Note the double meaning there; he does most of his work in darkness and/or at night.
Superman, on the other hand, is mostly out and about during the day. He's a bright, shining beacon of hope and promise. He has ridiculous amounts of power, and hangs out up in the sky. He is, in short, the Sun(and, in particular, the Last Son of Krypton). It's no accident that in many versions, he's solar powered; the power of the Sun incarnate.
So when the Knight meets the Son, we have a dawn. It's just that easy. But, like so many things with the Justice League setup, they haven't laid the groundwork. Given that he is being rebooted, Batman is yet to be shown to be a Dark Knight. Man of Steel really doesn't sell the Sun angle for Superman. Something as minor as changing that title to Last Son of Krypton instead would provide a connection, however tenuous. But it's not there, and they're just diving right in as if it was.