A few comments and then an answer to the OP.
I don't see how an eInk Kindle, or Nook, is more made for reading books than newspapers. How the customer uses it is up the customer. I'm sure more customers are using them for reading books than newspapers, but that's not inherent in the hardware. As for what it is made for, it is made for enriching the companies which make and sell it
I find it is good for reading books, but the greatest superiority over paper, to me, is for reading essays too long to comfortably read on a computer. Also, I am glad to no longer carry around, and fill my trash with, newspapers.
As for browsers, I wouldn't say there are browsers for eInk in the same way there are browsers for tablets and larger computers.
One way to start seeing what an eInk web interface works well with is to go to:
www.readingthenet.com
Then click on Book of the Web.
I have only used this with eInk Kindle models, but it may work with others.
Browse on a computer, and read on a reader. For one way to do this, go to
www.longform.org and set up the Send to Kindle buttons.