It is impotant to remember the way that this story functions as an allegory in order to highlight the dangers of human greed. Tom Walker, along with his wife until her unfortunate demise, is a character who is obsessed by greed, and therefore Irving uses him as an example of the dangers of greed and to show where such greed will lead. Note how he is described at the beginning of the story:
He had a wife as miserly as himself; they were so miserly that they even conspired to cheat each other. Whatever the woman could lay hands on she hid away: a hen could not cackle but she was on the alert to secure the new-laid egg. Her husband was continually prying about to detect her secret hoards, and many and fierce were the conflicts that took place about what ought to have been common property.
Tom and his wife together take greed and avarice to extreme lengths, even trying to cheat each other out of any wealth they can get their hands on. It is no surprise then, that as Tom makes his bargain with "Old Scratch," that greed should only increase until his own end. Greed is shown through this allegorical tale to be deeply compelling and a real danger to virtue. As with all allegorical tales, the greed in this short story is exaggerated to highlight the danger, which is why Tom Walker does not change at all throughout the entire story: he represents greed and its danger to humans.