] Sometimes unwelcome changes can be for the best, though, and I think Jane's time in Bath was one such case. Surely the Bath scenes in her novels would not have been as convincing if she hadn't had the opportunity to live there?

I agree. When she first visited she liked it well enough - a little like Catherine Morland - but she couldn't stand to LIVE there. She loved her home where she'd grown up and had friends and country walks too much.
Certainly, when I was in Bath, the people at the Jane Austen centre said she stored up follies and characters in Bath, that successfully poured out when she left. The city was a great asset to all her books.