I would think that one would want to sell even at $0.01
You definitely don't want to do that. You're going to be overwhelmed with support requests (for an e-book, even!) from the least competent potential users imaginable. Moreover, you're going to blunt the reason for writing the book in the first place, because the people best positioned to get value from the book will not do so because it is too cheap to be taken seriously as business advice.
You are right for $0.01 cost, but I wonder if that changes for $0.01 profit. What if your COCA (cost of customer acquisition) eats all but $0.01 of the revenue ? You are bringing in positive marginal revenue, and you don't have the downside you mentioned. Of course, you have others, such as this cost structure means you're making someone else rich, not yourself, and it's a very fragile situation, you can't absorb COCA increases.
You definitely don't want to do that. You're going to be overwhelmed with support requests (for an e-book, even!) from the least competent potential users imaginable. Moreover, you're going to blunt the reason for writing the book in the first place, because the people best positioned to get value from the book will not do so because it is too cheap to be taken seriously as business advice.