http://legal-dictionary.thefreedictionary.com/Paper
which are protected from being searched by the fourth amendment:
"The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."
(I quoted the modern legal definition of papers, but the proper thing to look up is the colloquial definition of papers at the time the constitution was written. Does anyone have a good reference for how the founders of the US would have used the word "papers"? It clearly included legal and accounting documents, but e.g. was it broader than that?)
Assuming you have perfect recall, and answer all of their questions truthfully, it will still take time for them to troll through all of your memories and actions.
They can do the same with a telephone / laptop in minutes.
Answer two: perfect recall
You can't recall everything perfectly, and you don't write everything down. So after a while, they won't have anything to go on. "What did you do in Thailand last Wednesday?" ... "I dunno, I got drunk with my friends?"
Versus "we searched your phone and you took pictures last Wednesday of someone who looks underage. Please turn around for the handcuffs".
In general, I have everything to hide from state actors with near-infinite resources, zero accountability, a deep understanding of the law (i.e. how to get you for almost anything), and their own personal agenda to push.
They should need to prove to me why they need to look at my stuff.
Giving access of that over to a government agent is like handing them a diary of everything you ever thought, a list of everyone you ever met, a record of everywhere you ever went, a list of every book you've ever read, a list of every medication you've ever taken, a list of every game you've ever played, a list of every off-color joke you've ever cracked with friends, etc.
Would you hand that over on paper?