Not my experience at all. I regularly lend e-books from my city's public library, and they usually have hundreds of "copies" available for popular titles, and even for less popular or even niche titles I rarely have to wait more than one week.

It is a bit ridiculous that "buying copies" and then imposing artificial scarcity on these is the best mechanism that libraries and publishers have figured out to compensate content producers, but I'm optimistic that they'll eventually figure something out.