Using ambiguity as a central technique to the narrative and style of the novel, Nathaniel Hawthorne's The Scarlet Letter is intended to tell the story of Hester and Dimmesdale in a way that instills in the reader an ongoing sense of wonder and curiosity; this hunger for further knowledge never becomes truly satisfied, opening the door to a myriad of possibilities and assumptions for further literary analysis. This universal quality is what makes the narrative "work".
The third person narrator is omniscient. This means that the narrator knows information about the main characters that the characters may not know about themselves. This third person omniscient narrator can actually sympathize with the protagonists as well as not sympathize with the antagonists. In the case of The Scarlet Letter, it is clear that Hester's story is told in a sympathetic tone.
Moreover, the narrative involves a fictional "primary source" described as
a large portion of ... pages [that] came into [the narrator's] possession.
This colors the novel with veracity and gives strength to the story; having a document that "certifies" the existence of Hester Prynne conveys the need to compare our here and now with that of Hester's, so that the mistakes of the past are never repeated again.
However, if the story had been told from a different perspective, it is possible that the reader may have acquired much more information than what Hawthorne provides. For example, had Hester been the narrator, we would have understood what drove her to the unthinkable act of committing a sexual indiscretion with the town's most respected elder. If Dimmesdale were the narrator, perhaps he could have given the reader some insight as to how he really feels about Hester; for, we never really get to know if he loves her truly, or if he is bound to her by guilt and duty. Chillingworth and Pearl could have also given very interesting accounts of the events, since they were both equally satellites in Hester Prynne's world.
Yet, too much information would have partialized the novel and may have even taken the focus away from that seemingly supernatural symbol of shame which is the scarlet letter, itself, as well as from the enigmatic woman that wears this letter with such strength and mystery of character.