That, and an enormous selection.
"Reading books on phones is awful."
It depends on the phone. Many people are perfectly happy reading for hours on a phone screen, particularly if they can choose the foreground/background colours (e.g. white on black for someone with an AMOLED screen).
"Reading them on Kindles is the closest screens can come to reading on books."
Well, in terms of display, it's the closest screens have_come, but it's unlikely to be the closest screens can come.
But, the thing which makes reading on a Kindle Paperwhite a pain for me, is that I can't flip through the book. Page turns are slower than on a paper book. I can't use my fingers to mark two different parts of the book, and move rapidly back and forth. Oh, and why can't I view images inline with the text?