Library of Congress, British Library, Bibliothèque Nationale etc choose to save everything they are mandated to, and a fair bit extra besides. That includes everything published. They don't save their water cooler chats, personal letters and everything sent by post, everything said on the phone or Facebook, etc.
The bar - perhaps found accidentally - seems quite important in deciding what must be archived, and what probably shouldn't.
Archives of personal letters and ephemera, preserved in manuscript/special collections libraries, are incredibly important research sources. This often includes letters which were never meant to published. LOC had a project to preserve every tweet (published to the world) until a few years ago - who knows what tweets might be useful to future researchers?
And yet, hundreds of years later historians and linguists crave for letters, and post, and telegrams to get a glimpse of actual life outside official publications.
Sure, and a hundred or more years later the family of the author, or relatives of the recipient can decide to release the family letters or telegram from WW1 or the US Civil War etc. That delay, usually at least until the correspondents have died, is important. The affair, the less than ideal belief, and all that other imperfect demonstration of humanity can no longer hurt or embarrass. It ceases to be private and personal and moves into the historic.
Releasing whilst the probably famous sender is alive is most often in the realms of to do damage, simply tasteless or paid for revelations in the gutter press.
The bar - perhaps found accidentally - seems quite important in deciding what must be archived, and what probably shouldn't.