The answer to this question depends a lot on the particular collection of documents that you are looking at. Someone like Samuel Hartlib (ca. 1600-1662), whose vast collection of correspondence is now digitized (you can check it out here), does very much fit the model of the person you described. Many others like him kept correspondence and other documents to publish memoirs or chronicles. They could refer back to these letters as a way of verifying information, especially in the context of rumours spreading by word of mouth.

That brings up another reason so many letters survive: institutions of all kinds would collect and hold onto them to keep up with the news and trade information. The letters of Venetian ambassadors reporting on events of the countries that they were sent to are an invaluable source of information on the political goings-on of 16th century Europe. Sometimes these kind of official letters could be printed or copied and circulated as a way of spreading news, or propaganda. The famous Jesuit Relations for example were circulated as a way of drumming up support for French Catholic missions abroad.

Even if you didn't plan on publishing an account of your life, or had some official reason to hold onto your correspondence, you might hold on to letters just for your own personal records. If you regularly corresponded with someone, you might hold onto those letters in case you wanted to refer back to something. This is why collections often include both diaries and correspondence (e.g. The Diaries and Letters of Phillip Henry) which document a lot people's day-to-day life. Just like you might save an important email nowadays, so too did people in the past hold onto letters for a number of reasons. Conversely, they may have thrown away many more, just like we delete many non-important emails, but because they no longer exist we can't really say too much about them.