It's probably not as bad when its paper copies of private information because most possibly its not stored on the internet. Im not someone who likes having to hand over all my private information to anyone. You just have to trust it never gets into the wrong hands.
Internet stored data would probably be the hardest to keep private.
Doing things by machine is cheaper for mega corp, and the public sector. I don't think they will be going back to keeping track of pieces of paper by hand.