What importance does Miss Prism have in The Importance of Being Earnest by Oscar Wilde?

Despite her inauspicious beginning as Cecily's ironically unintelligent tutor, Miss Prism ends up being a hugely important character in the play, because she turns out to be the woman who erroneously deposited Mr. Jack Worthing in a cloakroom at Victoria Station, the Brighton Line, when he was an infant. Jack never knew who his parents were because he had been found in a handbag given to Mr. Thomas Cardew in place of his own. Mr. Cardew kept and raised the baby until his own death. Later in the play, when Aunt Augusta visits Jack's home to retrieve her daughter, Gwendolyn, she hears someone speak Miss Prism's name, and she remembers Miss Prism as the servant of her sister's family, the nanny who disappeared with the infant one day and never returned. This prompts Miss Prism to tell the story of what happened to the baby, the baby who turns out to be Jack, and when Jack produces the very handbag that used to belong to Miss Prism, it confirms his identity as that baby, meaning he is Algernon's brother, Aunt Augusta's nephew, and Gwendolyn's cousin.  As he has now acquired parents and pedigree, he is granted permission, by Aunt Augusta, to marry Gwendolyn, which was his goal from the beginning of the play. The revelation of Miss Prism's identity and history makes both Jack and Gwendolyn's and Algernon and Cecily's weddings possible.