The answer probably lies in the need of an alternative-history writer to provide as much factual detail as possible to counter the unreality of the basic scenario. All fiction is premised to a degree on the desire to create for readers the illusion of belief, even while they know, presumably, that the story they are reading is untrue. Yet most novels take place within a world where the large-scale public details of life conform to reality. They could have happened as written, because the reader has no evidence to prove that the story he or she is reading is false. Alternative histories are different because everyone knows that they are premised on things that didn't happen. Therefore the writer needs to anchor such stories as firmly as possible in whatever is real in order to give the illusion of reality to the entire book, including the unreal parts.
In The Plot Against America, Roth employs the actual fact of himself as an eight-year-old and of his family in Newark in the early 1940s. He could have just as easily used, say, his Zuckerman persona as narrator, but this would have added another fictional level to a plot already based on what we know to be a fantasy-like recreation of history. By using his real self as protagonist, the illusion is strengthened that this could all have possibly happened as related.
There is another dimension to alternative histories often overlooked. Americans in general are not known for being especially knowledgeable about history, even their own history. Many readers can be reflexively dismissive of alternative histories, simply because they know that such events did not occur and presumably could not have occurred. But what about people who don't even know basic history? The Plot Against America occurs in a (now) still relatively recent period—only about 80 years ago. But what if the book continues to be read at some future point where the events of World War II are no longer well-known to the general public ? One can't be sure that even now, most people know the actual facts in any detail. In such a case, Roth's book could seem absolutely real, especially because the author is Philip Roth and the narrator is "Philip Roth." The book could then seem indistinguishable from a factual memoir, in spite of being a novel and an alternative-history novel at that.