The Lyme chapters are all about friendship and cooperation -- very different from "the usual style of give-and-take" which Anne witnessed in her own surroundings so far. Here Anne finds herself in the company of reliable and intelligent adults, and there is a feeling that for the first time she is an equal among equals.

In the beginning of the novel, Frederick Wentworth is thought of as a man without connections. In the Lyme chapters, his connections are fully disclosed, so to speak. The Crofts, to whom Anne and the readers are introduced earlier, and now the Harvilles and Benwick -- these are the connections worth having.

I think that even if Anne did not meet Mr Elliot in Lyme and even without a prospect of Capt. Benwick as a potential suitor the tenor of the Lyme chapters would remain the same and their importance would not diminish. By the way, when Lady Russell wants to get Anne to Bath to be "more known", she is primarily concerned with marriage prospects. Anne does not go to Lyme to look for a husband. She does find there a new world which she admires and wants to be part of.