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.

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.