Why would another point of view in "The Lottery" not be as good?
First person narrators are judgmental. They don't necessarily try to be but they are. Look at Nick in The Great Gatsby, or you're in 9th grade, maybe you've read The Scarlet Ibis. The narrator is the brother of the main character and he inserts those sibling disappointments and frustrations that we all experience. This makes the story real and easy to relate to.
With a first person perspective, you feel their situation from the onset of the story. This plot in The Lottery is designed specifically for you to receive a shock at the end. My students' jaws drop as we get to the end of this piece... a lottery suggests a winner for the positive, usually of money! If we received a first person point of view, we would feel their tense nerves as they told the tale. They would likely give it away. It would be an entirely different mood.
In this story, the point of view is that of an observer who is not able to know the thoughts of the people involved. I think there are a couple of reasons why this is a good choice.
First, if we were seeing things from the point of view of a participant, we would be more likely to know what is going on -- what happens to the "winner" of the lottery. Then there would be less suspense.
Second, the narrator is totally unemotional. This adds to the feeling that what is happening is totally normal. That really helps to make the central horror of the story (evil in a very normal setting) clearer to the reader.
If an omniscient or first-person point of view was used, it 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. Thus, 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 chose an extremely appropriate narrator for her short story, "The Lottery."