What is appropriate about the poem read by the house in "There Will Come Soft Rains"?

Bradbury's story, which is set in a post-apocalyptic city that has seemingly been charred by an explosion (presumably nuclear), is a fine example of dystopian literature. It also contains quite a bit of irony. It is ironic that Teasdale's poem is used, since the poem itself appears to mirror the fact that humankind has been annihilated and life continues on without noticing that people are no longer there. The poem seems to point out, rather indirectly, that while humans may consider themselves to be the centers of the earth and the things that happen on it, nature may tend to think of people as simply another cog in its machine that it can do without. This is also supported by how the house continues to labor on its own--without involvement or interference from humans.

The poem "There Will Come Soft Rains" is a short poem by Sara Teasdale, and it makes an appearance in Bradbury's short story of the same title. The poem is about nature's lack of care about the presence of humanity and the wars that humanity fights.

Not one would mind, neither bird nor tree,If mankind perished utterly;
And Spring herself, when she woke at dawnWould scarcely know that we were gone.

The lines listed above flat out state that nature simply won't care if mankind ceased to exist.
The poem is a good choice for this story because it further highlights the actions of the home. The house doesn't realize that it's hanging on by a thread, nor does it realize that the human occupants have all been killed in a nuclear attack. The house just goes about doing its daily duty. The poem does contrast the house too, which makes the poem work all that much better for this story too. The poem is a very peaceful sounding poem. Since nature doesn't care about humanity one way or another, nature just goes about its peaceful business. There is no worry or concern; however, as the house continues its job, its actions become more and more frantic. The house is worried about keeping itself together so that it can continue to serve its human masters. Teasdale's poem shows that nature isn't worried about keeping itself together for the sake of mankind.