Except requiring the physical book (or single book digital equivalent) controls the pace. If a standard checkout is 2 weeks, and if the book is always checked out, it will still take 4 years to hit 100 lends. And a thousand lends? Close to 40 years.
Be careful to avoid reasoning from an axiom that the way things worked when you grew up was the correct way. It's a pernicious psychological bias we all suffer from.
You over-estimate the lifespan of physical books and the physical stress of lending. 25–40 times is a more likely lifespan for a physical book. With digital lending, there are actually specific contractual limits on the number of lends and the cost per lend which vary based on the publisher. And the average number of lends per library book is probably close to 1.
Also note that the publishers' problem is not just the 3 months of waitlist suspension (supposed to offset the closure of physical libraries during the pandemic), but the practice of controlled digital lending of books scanned from physical copies (ie handing out a digital copy for each physical copy you've got sitting on your shelf) without additional royalty payments.
You can argue about the size of this group, but the counter argument would be that there is a valid fear that if it is normalized and allowed to continue, this group will grow larger and larger over time. You can argue by trying to compare this to libraries, but libraries still buy their copies of the book, and checking a book out from a library comes with restrictions that don't exist here. There really isn't a way to spin this where it doesn't result in some amount of lost royalties for the author.
There's plenty of totally reasonable hypotheses for why giving away content can be profitable OR unprofitable, and plenty of real-life examples of both as well. The fact is, with regards to this situation, we don't know, and this conversation shouldn't center around a problem that some people have only hypothesized exists.
Also it would a balance of what was free / what was purchased that would determine the net impact.
1. There actually is other material available from the author to buy. If there isn't, it's simply a loss. 2. If there is other material by the author, you have to assume the reader was not going to read any of the author's material without having access to the free book first. 2. If additional material exists, and the person would have never engaged with the authors work without a free "trial" of their work, less than 100% of people who access the free material will go on to buy additional material. Some because they are uninterested, some because they don't want to or can't purchase it for the same reason they couldn't purchase the original. In the former case, thats a net loss. In the latter, its a wash. 3. Even if there is additional material to buy, and even if the reader only becomes interested in the author's work through the free book, and even if the reader is inspired to go out and buy it after reading it, it only offsets the original lost revenue of the first, free book (assuming they are priced similarly). So its only if a reader is inspired to go out and buy at least 2 more works by the author that they would actually become a net positive for the publisher/author.
Clearly the number of people accessing the free material who would actually be a net positive for the author/publisher is quite small, and the free book in general would almost certainly be a net negative. You can do all the mental gymnastics you want, but at the end of the day, its still theft. People will argue that publishers are all rich and so we shouldn't care, but thats a different argument, and doesn't apply to the majority of authors who don't actually make that much money.
The actual issue is much more complicated.