This is covered by first sale doctrine. After the library owns that book it is theirs and neither the author nor the publisher is entitled to anything when the book is lent.
I believe most former Commonwealth countries work like that.
Here's the info for Canada:
https://publiclendingright.ca/
It's not a huge amount... minimum $50/book/year, maximum $4,500/book per year, but I suppose it's significant if you have, say, 20 books, each bringing in the maximum.
It's a flat rate, though, not a per use charge.
Why not? That's how everything else works, at least in the US. e.g. my local hardware store will rent to you a variety of tools (which they also sell) or even trucks. They don't need to compensate the manufacturer for each rental; they just buy it like anyone else would. Even Netflix got their start buying DVDs and mailing them to customers to rent. As far as I know they have no requirement to pay ongoing fees or establish a licensing deal to do that (and apparently they have better selection for dvd rentals because of that).
We're talking e-books ("concurrent check out"), and they certainly do.
https://www.pewtrusts.org/en/research-and-analysis/blogs/sta...
> While consumers paid $12.99 for a digital version, the same book cost libraries roughly $52 for two years, and almost $520 for 20 years.