When writing "The Lottery" Jackson's use of "common people" and lack of specificity in time period, location, etc is purposeful. She wanted the themes in the text to resonate and be timeless. If she used more sophisticated people, the story may have lost its impact on the reader for a few reasons.
In "The Lottery," the people are characterized by the devotion to tradition. The lottery is a part of the town's "civic activities" like "square dances, the teen club, and the Halloween program." Although elements of the lottery have evolved to accommodate the growing population, the black box remains a constant. In fact when it is suggested that the black box be changed, the town objected because "no one liked to upset even as much tradition as was represented by the black box."
It is this blind devotion and adherence to tradition that allows the lottery to continue year after year. At one time, there may have been a religious significance to the sacrificial ritual, but no one remembers or acknowledges that function anymore. Even now, some townspeople admit that others are ceasing the antiquated tradition:
"They do say," Mr. Adams said to Old Man Warner, who stood next to him, "that over in the north village they're talking of giving up the lottery."
Old Man Warner snorted. "Pack of crazy fools," he said. "Listening to the young folks, nothing's good enough for them. Next thing you know, they'll be wanting to go back to living in caves, nobody work any more, live hat way for a while. Used to be a saying about 'Lottery in June, corn be heavy soon.' First thing you know, we'd all be eating stewed chickweed and acorns. There's always been a lottery," he added petulantly. "Bad enough to see young Joe Summers up there joking with everybody."
Jackson portrays this sense of respect for tradition as a universal trait. By creating characters who are not sophisticated or of a different class, her argument is valid. Had the characters been more sophisticated, wealthy, or powerful, the reader would not be convinced that the motivation for maintaining the sacrifice was simply out of respect for tradition.
There are others that interpret the text as a demonstration of the worst of mankind. The lottery is a prime example of human beings' willingness to find a scapegoat. This is supported by the town's willingness to stone Tessie Hutchinson, and their inability to feel remorse for her as she pleads "It isn't fair." Once again, if the characters were more sophisticated, wealthy, or powerful, the reader may not empathize with Tessie. They may be more apt to blame her sin for her punishment rather than see the ills of human nature.
The ironic twist is setup by the tone in the story. There is nothing somber or morose in the tone to indicate that Tessie will be harmed let alone stoned to death. The tone of the text emphasizes the ubiquitous nature of the event and how essential the characters feel the event is.