If you leave your papers at home, you can't easily access them by logging in on someone else's papers.
Photocopying seems analogous to copying files at first, but consider the costs of photocopying something. In addition to the expensive machine, you need paper and toner...
Bits are a hell of a lot more fickle. I can't ever know for sure what will happen to my data that thousands of companies have harvested online about me, even if I ask every one of them to delete it all.
I can't have machine learning algorithms run on my paper to target me ads, either.