I think Elizabeth is plain mean in many cases. She is a bully. Imagine other Austen characters who are merely "thoughtless and self-centered" (Emma springs to mind) saying the things that Elizabeth says. It just wouldn't fit because they are merely thoughtless and self-centered. Emma would never say that a member of her own family was unwanted! The thought is shocking. And had she made the caustic comments that Elizabeth makes about Lady Russell's dress, outre' way of sitting and reading habits, I'm sure Mr. Knightley would be there to scold her and tell her "badly done." In fact Knightley great scolding of Emma for her treatment of Miss Bates, had mainly to the difference in power between Emma and the spinster. It was the fact that she was poor and in a weaker position than Emma, that bothered him. That was bullying and you can bet he nipped it in the bud.
Elizabeth steps over the line and picks on some weaker than herself, her sister Anne. These moments are thoughtless and self-centered, but they are worse than that too.