To which, many librarians many librarians would respond, "Oh come on, it's the 21st century. Being a librarian isn't just about books anymore. It's mostly about mostly about managing knowledge and information in all its forms - most of which doesn't involve books at all."
This is certainly true for me - over the past two years, I haven't been required to even handle a book, let alone read one!
At the same time, I suspect that the source of said angst isn't so much the misconception that being a librarian is all about loving and reading books, but rather about wishing that this were actually the reality of being a librarian.
I remember working in school and public libraries, and being frustrated by the fact that here I was, surround by books, and I would spend 80% of the time either finding books, shelving books, checking the order of spine labels of books on the shelves, or providing customer service (i.e. directing patrons to the toilet or negotiating disputed library fines), when what I mostly wanted to do is share my love of literature with the others in the library. Of course, I also cared about community development, information literacy and local history, but it was mostly about the books.
And yet, I still hold on to my bookishness as an integral part of who I am as a library and information management professional. I attend (and occasionally work at) literary festivals. I read a bit - not as much as I'd like to, but apparently much more than the average person. I review my books, reflecting on my experience as a reader, and on the book's own literary merits against its contemporaries. I engage on twitter chat sessions, particularly on YA literature. I share my experiences with others, and engage them in gleaning their own thoughts.
Not only because this is what brings me some degree of happiness in my life, but when that dream job comes along when I get to be both innovative in my information professional skills and pursue my bookish passions as a core part of my job - I will be ready.