> Elcock said he believed Herzberg may have been homeless.
I do not think that Herzberg possibly being homeless adds any meaningful information. On the contrary, I feel this may subtly support unconscious prejudices.
In this sense, it is a possibly relevant detail of the story.
Can't speak for the reporter who asked that, but I can take a guess about why it was asked. The victim's death and identity has been known for half the day. Her being homeless might possibly figure into next-day stories about why we haven't heard much from grieving family members. But yes, you're right, it is a detail that will figure into people's prejudices.