Why is the setting of "Contents of a Dead Man's Pocket" so important?
You have asked a really interesting question, because to me the two different settings of this terrifying short story act symbolically to suggest the two different ways of living that Tom struggles between. The ledge, of course, seems to represent the cut-throat struggle of climbing to the very top in his company, which Tom desires so much to do, and the apartment represents the safety and warmth of not choosing to live a life dedicated solely to work, but focusing on enjoying life and marriage - the important things of life. For me, then, it is absolutely key to think about how Tom changes from the start of the story when compared with the "new" Tom that we see at the end of the story, who decides to leave his work and go out and find his wife Clare - who he so willingly let go by herself before.
It appears that Tom has experienced the reality of the cloak and dagger world of work, where every step could result in your downfall, symbolically through his voyage out of his apartment onto the ledge. He is so grateful for getting back into his apartment that he now doesn't want to live his life that way anymore. He has changed so much that he is even able to see the irony of the situation when the same paper he has just rescued goes out of the same window again when he opens the apartment door to go out:
As he saw the yellow paper, the pencil flying, scooped off the desk and, unimpeded by the glassless window, sail out into the night and out of his life, Tom Benecke burst into laughter and then closed the door behind him.
We see a very different man who, we are sure, will live his life in a very different way after his experience.