I've been hearing about paperless offices for twenty years or so. I don't think it will ever happen. As an accountant, I want a paper trail (as ballisic pointed out). We can reduce a lot of paper, but it won't go away.
Compare what it was to what it is. If you want to say that there will always be a tiny fraction of paper, maybe. But I agree that it's coming.
I do not have a Kindle or the equivalent, but I have read books on the computer and I see the winds of change. Books are better in that they always work in the light without batteries, they can be lost or ruined, but it's no big deal to set them down at the beach while swimming or drop them in the tub. They are more expensive than the ebooks now, so that spells doom.
Newsprint is a thing of tradition. It will die sooner than books.
I think the post offices will survive quite a while yet as it is still useful and what poor people need. But bill paying will change if society lets it. Companies hate generating paper and paying postage and waiting for their money. They will encourage technology that allows the poor to "save a stamp." It'll happen.
Think about this: coupons in the mail and newsprint are almost entirely dead. They have websites that encourage you to print your own at home. Eventually, you will be able to get the deal without the physical coupon, but will just scan your smartphone at the checkout. It's already happening at airports where you can print your own boarding passes at home or (often) just show your smartphone scan of your pass.