What if another point of view were used, how would the story be?
You might receive different answers to this question. I think that changing the point of view of the story might reduce some of its effectiveness. The sheer horror of the incident, of the event, is brought out by the third person nature. To have supplanted this with a more subjective narration would not be as effective because it would take away from the dramatic impact of what is happening. There is a feeling of helplessness that pervades both readers and characters in wanting to be able to stop this horrible tradition, but being unable to do so. This seems to me to be precisely what impacts us and the characters the most, and to have changed the narrative structure might take away from this.
Either an omniscient or first-person point of view would need to include information about matters such as the hesitation of the two men (paragraph 4) and the tradition of the lottery (paragraph 5). In addition, an omniscient or limited omniscient speaker would probably need to personalize Tessie Hutchinson more than at present. Hence, either of these alternative points of view would make the conclusion less of a surprise and more of a fulfillment of premeditated social brutality. Shirley Jackson's "The Lottery" is one of the most powerful stories in the short story genre.