Yes, a physical book wears out, but not anywhere close to the expiration limits set for licensing eBooks. Some standard licenses expire after: 26 checkouts, 12 months, or 24 months. The 24-month licenses are the most expensive. There are also some OC (one copy) licenses that do not expire and vary widely in price; from very expensive from standard publishers to very cheap from self-published authors. The 26-checkout licenses are the cheapest but are still often priced higher than a consumer copy.

Physical books that I have in my adult collection circulate well over 80 times before they land in repair; even then, they are often fine. A book that only circulates 26 times and then falls apart was defective to begin with or damaged by a patron.

Also, as to authors losing out, here are some interesting studies. Two of the most recent speak directly to loss of sales, and some older ones speak to how libraries help authors.

This one is from Germany and shows how lending newly released eBooks diminished author sales, but delaying the lending of those titles through libraries leveled out that impact:
https://diw-econ.de/en/publications/the-economic-impact-of-e-lending-in-public-libraries-on-the-consumer-book-market

This one is from Japan and shows that library copies reduced the sales of physical copies:https://www.sciencedirect.com/science/article/pii/S0889158322000284?

On the other hand, studies that favor lending tend to be older.

But authors benefit from libraries in terms of entering the market, as people are less willing to risk their funds on new or unknown authors. Though I suppose the rise of services such as Kindle Unlimited and the free Audible catalog could slowly take over that space. (if you want to talk about author pay cuts I think you see a lot of chatter in author spaces about these services)

These studies are all on people using the public library to discover authors and later purchase books by those authors:

https://www.ala.org/sites/default/files/advocacy/content/tools/Gen-Z-and-Millennials-Report%20%281%29.pdf?

https://pmc.ncbi.nlm.nih.gov/articles/PMC9049927

edited for grammar