Because she is Anne, I would consider that she would feel it her duty to write and she might make some effort to send a nice letter, but I am also sure it would not be enjoyed by either Elizabeth or Sir Walter even if it was. How much would Anne actually tell them? Would she feel it her duty to tell them of the arrival of Captain Wentworth? Would Elizabeth and Sir Walter actually be interested in the goings-on at Uppercross? We have read how little the people at Uppercross were interested in the family leaving Kellynch and I would think there would be no curiosity on the part of Elizabeth and Sir Walter about Uppercross.

The only items of interest to them might be intelligence of Lady Russell and the Crofts, and of particular shrubberies and flowers at Kellynch. It does not even seem very likely to me that Sir Walter would be curious about his other tenants or that Elizabeth might worry (Never!) about the status of the poorer tenants of Sir Walter. I imagine that although Mary might not want to write letters, she would want to be the first to know what is happening in Bath from received letters, but I think Anne would be bored to tears by the relation of the fluffy social events that I imagine Sir Walter and Elizabeth might enjoy. Other topics Elizabeth might write about would be how bad most of the Navy men in Bath look according to Sir Walter or an update on the state of Mrs. Clays freckles or perhaps that Sir Walter is still not looking with a favorable eye upon Mrs. Clay who is still in her proper place.