In 2011 Amazon started working with Overdrive to allow Amazon Kindle users to check books out of the library to be read on their Kindle devices. Any Kindle or Kindle App can now check out books from your local library. Approximately 11,000 libraries in the US allow users to check ebooks out using Amazon.
The main complain that I hear about OverDrive is that there are not enough books or the wait is too long. And that complaint is all about funding. Your local library system as part of their agreement with OverDrive, chooses the mix and number of books. My local library, Cobb County Library, went from about 800 ebooks in 2011 to about 8600 today. Most of those books only have one or two copies. As I was browsing, there were a few that had more, but Cobb County has chosen to have more books, rather than more copies. If you want more books in your system, then tell your local library, and comment to your local government about the funding. You are paying for these books, it is just that you are not paying for them directly, but through your tax dollars.