I imagine a lot of people would be horrified at this idea. Some would think this is a point where one crosses from frugality into cheapness. Are the books really a gift, or just another holiday obligation, as the recipient must make sure to get the book back to the library before it becomes overdue? Are the books really a gift, or just a way for the giver to pretend they gave a gift?
Well, I guess there is philosophy behind such gift-giving and the process will work best if both the giver and the recipient are ~on the same page~. If both agree that we do not need to personally and individually own everything that is useful to us or that appeals to, and that it is actually better to own less, this giving of borrowed books will work best.
That said, I have a friend who did this one year for all her friends. I thought it was great. Really liked the book she picked for me, too!

I was new in town. Returning the book became my first visit to the big downtown main library. So that was cool.