People consume fewer books than songs, though. I might listen to hundreds of songs in a month, but only read two or three books, so that $10/month fee is being split between very few authors. Say this means that an author gets $2/reader under this model. Is that unsustainable? It doesn't seem too different to me than what authors have always gotten in the dead-tree model.
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).
Agreed completely with your first paragraph. Your second point is key, and that's where I don't have enough information to really know how this plays out in the long run.
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.
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).