Amazon already has this button on books without Kindle editions -- just under the book's cover pic, there is a link to click to tell the publisher you'd like to see a Kindle edition of the book. It says: "Tell the publisher! I'd like to read this book on Kindle."
Of course, it doesn't force publishers to do anything, but presumably Amazon passes the info on to them.
The problem with this is that if like me you're in the UK and there
is a Kindle edition, but it's just not available
here, (and so many of the bestsellers
aren't) then the button doesn't show up - I've learned now that that's what the lack of a button means. I'd like to see a "Kindle this book in my country" button.