Also, the family was important enough for Superman to break someone's neck to save them, but not important enough that we don't see them ever again?
I don't really see why we needed to. We didn't know anything about them; they were just some random civilians who were supposed to be representative of humanity as a whole-- who all would have been killed the same way if Zod got his way.
In fact I kinda like that the big showdown involved not the hero's girlfriend or love interest like in most superhero movies, but just some everyday people who were in the wrong place at the wrong time.