Yes, a pirated book is often a illegal copy of a legal original. But every copy in a library is legally paid for - and they expect you to return the copies you borrow when you're done with them, because they would have to buy more otherwise. Libraries don't undermine copyright law, they depend on it for their survival.
But the damages are still done. By having a library where people can get a book for free instead of buying it, even though there is some throughput limits, they still make it so that the media is no longer consumed.
Imagine a pirating service which ensures that a given file is only being consumed by one machine at a time. So if I want to watch the newest blockbuster, I have to wait my turn, and once watched, I cannot watch it again (without getting in line). In effect, the movie is checked out a single instance at a time, just like how a library checks out a single book at a time.
The real damage from piracy comes from distribution, rather than consumption. Lending might do a small amount of damage, but as long as the inventory publishers have has been paid for somehow, they don't really care. They would care if libraries started running printing presses in the back and gave away extra copies for free, which were indistinguishable from the original, which is essentially the piracy model.
IANAL but I'm honestly not even certain that the piracy service you describe would actually be illegal, or at least that it couldn't be done legally.
