Passing e-books on to others does present a challenge. The difference is that when you give a copy of a print book to the library, you no longer have a copy of the book. If you give a copy of an e-book, you still have the copy on your hard drive so rather than sharing one copy of the book you have created a new copy.
I don’t agree with draconian DRM (digital rights management) processes that don’t allow e-books to be shared. Instead, I prefer to just remind readers that if they create and distribute additional copies of the books, they are cheating the authors.
On the other hand, I have no objection to readers having more than one copy of an e-book for their own or family use. There’s no reason someone can’t have different formats to read on their computer, an e-book reader (or more than one if they or family members have more than one), and a phone. That is like taking a print book from the living room to the bedroom to the den and reading in different locations.
In fact, when I create e-books for my publisher or my clients, I always create several different electronic formats and put them together in a single zip file. When a customer places an order, they download the zip file and can read whichever format(s) they want. Smashwords allows you to download any and all formats you want when you purchase an e-book and you can return and download again if you need to. Unfortunately, proprietary formats like the Kindle and Sony can be read only on specific devices.
It’s primarily the large traditional publishers who put DRM on their e-books. Most independent and self-publishers make their books easily available but simply ask readers not to make duplicate copies of their books. Most small publishers price e-books reasonably, and you can find lots of free e-books, especially public domain books. So you don’t have to spend a lot of money to read a lot of e-books.