The real problem is one of socialism. Government-run, taxpayer-supported public libraries prevent private business from operating bookstores and newsstands at a profit. A subsidized industry has a built-in advantage over entrepreneurship every time.
Ben Franklin's original lending library was a private enterprise with volunteers exchanging reading matter. It wasn't a state-run outfit like the public libraries of today. Moreover, public libraries are hangouts for stinking third-world types and the homeless. It's not a realistic scenario but I'd really like to see the government get out of the book and periodical business, thus allowing free enterprise to flourish in that sector.
I hope you're kidding. I don't think B&N (and Border's before it, and every other bookstore and bookstore chain) is having trouble competing with the public library. Public libraries have existed throughout the entirety of B&N's existence, and B&N was flourishing until Amazon (and the Kindle) came along and was able to undercut B&N on price. Blaming B&N's troubles on the public library is absurd.