Austen's fantastically intelligent revision produced the current ending: the letter which Captain Wentworth writes after he hears Anne declare that women stay true to their first loves. He is stuck in a parlor, surrounded by people, and responds to Anne's declaration with the means he has at hand.
It is the perfect pay-off for the novel and for these particular characters (the 1995 movie combines the two endings quite effectively).
Letter-writing was an omnipresent activity in Austen's world. In many ways, it was more like "tweeting" than even modern-day emailing. Consider Pamela in Richardson's novel, feverishly writing her parents every detail of her life. Consider Darcy's letter to Elizabeth or Jane Bennet's continual letters to Elizabeth. Consider the romantic poets who were constantly exchanging letters, many of which were written on the backs of poems or in the margins of prior letters (paper was a precious commodity). For that matter, consider Jane Austen's letters to her own sister! (The comparison to "tweeting" might explain why Cassandra burned a number.)
For Austen as for Shakespeare, letters are the ultimate truth-tellers. In Much Ado About Nothing, Shakespeare uses his characters to argue that what one sees or hears cannot be trusted, only what one writes. When Benedict and Beatrice exchange poems at the end of the play--after another prideful argument--Benedict makes the point clear:
"Here's our own hands against our hearts!"