Mrs. Bennet doesn't want to eliminate just the most likely competition to her daughters' chances; she wants to eliminate all competition.

"I do not believe Mrs. Long will do any such thing [introduce the Bennets to Mr. Bingley as she promised]. She has two nieces of her own. She is a selfish, hypocritical woman, and I have no opinion of her." (Ch. 2)

Charlotte is just the most obvious competitor, both in Mrs. Bennet's mind and in the neighborhood. Charlotte for her advanced years (in terms of Bingley's age) and looks less lovely than Jane and Lizzy, is still intelligent, socially adept, and thrifty (if she takes after her mother, who must make do on Sir William's not-overly-large savings). In addition, her father is a knight, which may attract some suitors; and to Mrs. Bennet's chagrin, Charlotte's mother is Lady Lucas, with which Mrs. B seems to have an ongoing game of one-upsmanship.