In "There Will Come Soft Rains," why is this line important: "The house stood alone on a street where all the other houses were rubble and ashes"?

The house stood alone on a street where all the other houses were rubble and ashes.

In addition to the above answer, I might just add that the line also actually introduces an important character in the story: the house. The house has survived the holocaust even though the inhabitants are nothing more than five spots covered by charcoal on the wall. The house carries on as though the horrors of human madness can't touch it; as though it were an individual, really--the last individual.

The return of the dog is another thread of the idea of the last survivor. Yet, the dog is dead within an hour. The house too, the last survivor in a decimated neighborhood, will die within its own metaphorical hour, which comes soon with the upwelling of the wind of nature. This ties back to the dog which is by definition a part of Nature. The summation is that neither nature nor machine can withstand and survive the genius of man turned to madness.