Some of the comments depend upon where you are
Libraries are not free. They are, at best, pre-paid by local taxes. The build, maintenance and staff yes. In some countries publishers have to give free (yes 100% free, no cost etc..) copies of books to libraries.
You could start by not saying that public libraries are free.
may want to check my comments. I NEVER mentioned "public libraries" - there are many types of libraries (company, private, academic,etc..) as well as public.