we have this reference to Mary:

"...she was eagerly succeeded at the instrument by her sister Mary, who having, in consequence of being the only plain one in the family, worked hard for knowledge and accomplishments, was always impatient for display."

I think Mary felt inferior to all her sisters when it make to looks and tried to make up for it by pursuing accomplishments, but she "had neither genious nor taste" and "vanity had given her application", but she was also full of conceit and affectation. Her personality did not help her deal with the differences between her and her sisters, so imo, if she was left out it was partially her own shortcoming.