I agree that it's a better user experience than the non-digital alternative, but I'd like to see digital books at libraries be available for free to anyone who wants it at any time, without any arbitrary restrictions whatsoever.
Oh yes - my favourite local library branch [1] is mostly volunteer-run and as such was the last one to get computerised lending, so any books older than ten years or so still have that paper slip in the back onto which the due date used to be stamped. Looking at those, quite a number of books (and not just the ultra-popular ones) would have already expired if they had been subject to the same lending caps as digital books, but in practice are mostly still in an okay (or even a bit better than just okay) condition that still looks good for quite some more lends.
On top of that, it seems that some publishers now use licenses that simply expire after a fixed term (two years or so!) regardless of the number of lends (compare https://news.ycombinator.com/item?id=20982315).
[1] A former US Army library in Germany that was donated to the city when that particular Army base was closed in the mid-90s and now effectively functions as a dedicated English language section of the regular city library.
Also my library often has 10-20 copies of a book but only 2-3 "copies" of the intangible version.
Wasn't sneak n' peek on library records one of the sticking points of the Patriot Act?