If this model takes hold, the thing that may need to change is the book itself. The economics of subscription suggest a shift in incentives away from the years-long creation of 300+ page tomes, and toward serialization or shorter forms. It behooves me, as an author, to have 10 or 20 "books" (or serialized installments) floating around the system each year, casting a wider net, than to bet the farm on one book a year.
This has already happened. For smarter writers, Amazon's distribution model killed the Big Novel model and pushed them to a cheap installment-of-the-month model.
Dickens used to publish like this (not through Amazon, obviously) so it's not necessarily a bad model.
But writers are notoriously bad at business, which is why mainstream publishing contracts have gotten away with being so larcenous and exploitative for so long, and why it's been so hard to make a living out of fiction unless you top the best-seller lists.
Amazon changed that. A lot of authors were finding they could support themselves from self-published fiction, full-time - which was never possible with trad-pub contracts, because they give mid-list and lower writers a tiny advance, insultingly small royalties, and take up to two years to get a book into the stores after the writing is done.
Those self-pub writers are going to be looking at this nervously to see how it changes the economics again.
Not that they should be surprised. A lot of people predicted this.
"Those self-pub writers are going to be looking at this nervously to see how it changes the economics again."
I dunno. For the time being, many of them will need to think carefully about how this shift changes things. But they're the ones who stand the benefit the most here. Self-pubbers who have been playing a volume and catalog game -- as the more successful ones have for years now -- are going to understand how to play this new game. Traditional authors, who've never been much for business or self-promotion as a group, are going to freak out. People with large catalogs are going to win. People with one or two Big Novels are going to lose (unless those Big Novels happen to be bestsellers already). People who can produce reams and reams of new material every year, nurturing mailing lists and activating fan bases, are going to keep doing that, and it will keep serving them well.
It also seems like the incentives depend on how Amazon is compensating authors: a fixed per-book fee would incentivize splitting large books into small pieces, so as to collect the fee multiple times, while a per-word or per-page fee would be more neutral (assuming that Amazon tracks how many pages actually get read, e.g. Piketty would only get credit for the tons of people who read his first chapter).
What we can reasonably predict, regardless of compensation structure, is that Amazon will gain more and more buyer power over the book market, especially vis-a-vis a fragmented ecosystem of thousands of self-published writers. This gives the company theoretical power to drive royalties lower. Whether Amazon exercises that power, and to what extent, depends on the royalty model. Whatever the model, I still think this incentivizes authors to produce a higher volume of shorter works, as opposed to a lower volume of longer works. Piketty, in this model, would be better served breaking Capital in the 21st Century into two or three smaller volumes. As a side benefit, his wider net would allow him to increase the statistical likelihood that he appears in any given reader's 3-4 choices a month. (Holding aside the ability of the reader to read more per month if books get shorter.)
And that may actually be a better thing for readers and writers. More digestible, approachable, less intimidating books might actually be consumed and read more. Sort of like breaking a bigger meal into several courses. I can almost guarantee you that the majority of people who bought Piketty's book have only skimmed a few parts here and there. Which is suboptimal from the perspective of Piketty's mission, which is to transmit the knowledge contained in his book. So shortening or serializing the form might help get the book actually read more often.
This is a prime example of how this development could end up hurting consumers. For those of us that strongly prefer 'deep' books rather than ones released in chunks, the economic disincentives facing authors of such works suggest that there will be fewer options available in the future.
Of course, this isn't unprecedented. Dickens used to publish serially (partly because publishing and copyright enforcement was a bit of a free-for-all back then), and even the book-length versions of the novels had to be subsidized with advertising to offset the piracy losses. I have a copy of Great Expectations with advertisements for laundry soap and brass polish, which were aimed at the servants who were the target audience for the book.
But people also don't read as much books as they listen to songs, so naturally the royalty per unit consumed will be higher for books.