As much as I am in favor of a good education, I believe I have read that Jane Austen herself (except for the years she was at a boarding shcool that she did not particularly like) was educated mostly from reading the books in her father's library. Could Jane and Lizzy Bennet's good sense be more inherant than learned? Perhaps Lizzy reads more because that was her nature, not because of any formal influence from her father.

In MP, the Bertram girls and Fanny do have a governess. Fanny turns out well. The Bertrams, while they can list facts, have little moral sense and are proud.

Emma's governess, Miss Taylor, was more or less guided by her charge, rather than the other way around. Emma never finished reading the many lists of books she wrote up.

I believe Catherine Morland was educated by her mother and grew up rather ignorant, but was still sensible.