A look into the discussion on https://academia.stackexchange.com shows, that the admins are not very motivated to talk about library privatization. As a reaction to my question, they asked back for references and questioned, if this has something to do with Academia overall. Perhaps I can deliver some details.
At first it is important to talk about the legal status of libraries. That means, it has to do who own a public library, the government or the stockmarket. This is important because lending is at first a business. Let us take a look in some business which are dealing with this subject. Since the 1980s Video rental shops are available, https://en.wikipedia.org/wiki/Video_rental_shop Alone in the U.S. the classical physial rental store has many million customers. In the recent years a new business model was founded, called online streaming service. This generates also lots of profit. And a very new business model is called ebook flatrate. That means, the customer is no longer buying a book, but paying a fee for reading it within a week.
What is the idea behind all these companies? The idea is, that on the one side some media like films, tv-series, books, CD-ROMs and computergames are available. The content was created by book publishers, game publishers and by hollywood. On the other side is the customers who is interested in the content and has money for doing so. Like in any business, both market participants are meeting each other and change money for services.
And now comes the surprising question: what has this to do with public libraries? The answer is, that public libraries are also offer books, DVDs and computergames. And the question is: why?
Or let me become more specific. The traditional Open Access debate is about digitizing library. This is not a major problem. Because for printed books and movies on DVDs in the future will be also a market. The more interesting question is, if a public library or a video rental shop should provide the media to the customer.
The most impressive example for an online library is Scribd. This service works similar to Amazon Kindle Unlimited and the idea is that the customer pays a flatrate for reading a book. The surprising fact is, that on Scribd all the books are available which are also provided by an Academic library. The difference is, that Scribd is a for-profit company. Is it possible to run a high-quality media lending service as a for profit company? Yes, the video rental shops, Scribd and Netflix are the best examples. These companies would gets lots of more customers, if the public library are also working as a for profit company.