You're not alone. Many authors are drawn to the idea of including letters in fiction. In fact, there's even a name for it: epistolary fiction. Some definitions of this term stretch to include diary entries and other forms of correspondence, such as email and telegrams. Whether you label it epistolary or not, you'll find all sorts of documents in fiction.
Annie Proulx's novel Postcards includes—yes, you guessed it—postcards from various characters within a more traditional narrative. In Tim O'Brien's novel In the Lake of the Woods, the unfolding action is interrupted by chapters called “Evidence," which include documents that shed light on the My Lai massacre during the Vietnam War and the main character's involvement in it.
Rosellen Brown's short story “Inter-Office" is written as one long memo to the mayor. It begins like this:
TO: The Mayor
FROM: Sid R.
These are not the promised notes form the Transit Authority meeting—sorry. I will not give them to Gail to type. She shocks and worries and mothers me enough already.
I have a couple of stories to tell you, Mr. Mayor, to drink down with your morning optimism. I am not going nuts. I am not trying to extort more pay or make the evening headlines or any damn thing.
Alice Munroe's short story “A Wilderness Station" is written entirely in documents, many of which are letters. From these, the reader can piece together the events and reflect on the different versions of truth surrounding them.
There's no limit to the documents you can include in a fiction. Tim O'Brien's In the Lake of the Woods includes court transcripts and excerpts from biographies of politicians and magicians' handbooks. Lauren Groff's novel The Monsters of Templeton includes letters as well as newspaper clippings, a family tree that's revised throughout the novel and even images—portraits, paintings and a photograph of a bronze statue.