For a start, being left at an early age mistress of the house happens to Emma and Eleanor Tilney, and yet they do not turn out so cold as Elizabeth (and Eleanor Tilney has a much more difficult father to contend with too).

Plus she is not left alone in the role, she can draw on Lady Russell's expertise if she likes. And it is not a matter merely of an annual week in London. For thirteen years had she been ....walking immediately after Lady Russell out of all the drawing-rooms and dining-rooms in the country. Thirteen winters' revolving frosts had seen her opening every ball of credit which a scanty neighbourhood afforded ... . I think there was some more social life going on in the country, limited though it may be compared to London.

What reason had she to think this was not set in stone? - Umm, that Mr Elliot had not agreed to it?

I read that sentence you quote as a bottom as more of a criticism. Elizabeth has never developed an interest in, say, assisting the poor, or in art or reading. She, like Mrs Elton, has no resources to bear a quiet life in the country.

But that brings on a second thought, what does this imply about JA's view of human nature and the possibility for improvement? At times JA seems to be quite a nature-over-nurture girl. Elizabeth has had more exposure to Lady Elliot than her younger sister Anne, but she has never developed any useful or absorbing skills. And she shows no signs of doing so, her disappointment in Mr Elliot does not lead to any reformation or to any sympathy to Anne on her engagement with Captain Wentworth. more than Anne could combat ... been possible to withstand her father's ill-will, though unsofted by one kind word or look on the part of her sister ... . The only characters in JA who seem to improve are the ones already quite good at the start, the fools remain fools. It's a bit depressing (maybe Catherine Bennet is the exception?).