Some critters like to eat paper.
Paper burns.
Paper has weight.
Paper has volume.
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...
It shreds too. This is a feature.
I can't have machine learning algorithms run on my paper to target me ads, either.
Paper needs no network coverage (not Wi-Fi)
Weights compared:
iPhone 6 4.55 ounces
Paper notebook (example) 3 ounces
Summing up the risks of flood+fire+critters you have a fraction of the risk for "falling to ground and break screen"+theft+malfunctioning.
You'll need a pen or pencil, though.