When I was a child, my mother helped out at a private library that definitely was aimed at making a profit, albeit a small one. It was sited in a small suburban shopfront, and was stocked with popular paperbacks, mostly romances. The mainly elderly female clientele hired books for a small fee, and were given an even smaller refund when the book was returned, which was a deposit on the fee for the next book taken out. It didn't last long as a commercial venture, disappearing when a branch of the public library was set up in the same shopping centre, attracting the public with free book loans and a much wider range of literature.
I witnessed a similar venture being set up in another town, about thirty years later, also in a small shopping centre with no public library branch. The speculator hired the venue, bought in many boxes of magazines and pulp romances, and set up shop. Her system was a little different. You bought the book, just as in any other secondhand bookshop, and when you returned the book, you were given a slip that served as a deposit on the next book you "bought."
I think the shop lasted about five months. This time, the public library was not a factor. What felled this venture was the quality of the offering. If you want to look something up, or borrow a book on some esoteric topic, you don't go to a little profitmaking library, because it is so highly unlikely to hold the book you need.
It is an accepted fact that a public library is a recipient of public funds, not an earner. In New Zealand, there are various methods of helping out the budget, such as interloan fees, reserve fees, late return fees, and borrowing fees for CDs, DVDs, and bestsellers. But these don't even start to get the balance sheet into the black.
Their aim is to make a profit themselves, while at the same time removing a financial burden from the city. The question is, how are they going to do it?
The librarians, for obvious reasons, are worried. The company asserts that libraries are often creaky antiquated organizations with inefficient service. "Our" librarians are going to be made to work, they aver -- which presumably means that the era of the librarian who becomes so interested in your research project that s/he devotes thought and time to providing active help is over. There just won't be time for that kind of thing. There are also dire suspicions that they are going to "clean out" under-used material.
Patrons are even more alarmed, to the extent of writing petitions. Publicly owned libraries are a cornerstone of democracy, they say. Whether they will succeed in fighting the juggernaut remains to be seen.