Why do you think the author gives human-like qualities to the house?
In the story There Will Come Soft Rains, the talking mechanical house represents humanity. Nearly every story in existence contains some sentient life, whether that takes the form of talking animals, magical beings, or just plain old humans. In short, most stories have characters.
There Will Come Soft Rains only has one talking character and this character is arguably not sentient at all. The house displays some awareness and anxiety, which are human qualities, yet it is distinctly not human. The house is programmed to serve its family and gives little, if any, indication that it possesses any thought or free will of its own. Therefore, the only talking being in this story is hardly a character at all.
The house represents the inhumanity of the world that constructed it. It symbolizes the advanced technology that helped destroy the human race. And it represents the cold efficiency of the world prior to the war.
The house did everything for the family that lived there and in doing so became just one of the many ways that humanity out-bred kindness. Instead of your loved ones surprising you with breakfast in the morning, the house does it for you and requires no thanks. Instead of spending time entertaining and coaxing your children, the house can do it for you. Instead of remembering your friend's marriage, the house reminds you. The house was made human so the people didn't have to be.
"'Today is Mr. Featherstone's birthday. Today is the anniversary of Tilita's marriage. Insurance is payable, as are the water, gas, and light bills.'"
In a world destroyed by nuclear war, a lone mechanical house that doesn't dream or love is the only thing left that even resembles humanity. The house represents how the technology that people make will outlive them. The house also lives on in denial of what has transpired. It knows that its owners are nowhere to be found, and yet it continues about its daily tasks just as before. It's blatant denial of the horrors surrounding it mirrors how people always manage to pretend not to notice the signs of their impending doom. The people who owned the house and others like them must have seen the signs of how catastrophic the war would be, but none of them cared or tried to stop it.