There are good and bad points in what you say.
Topic and name
From the name, I imagine a site about books could include questions about:
- Writing books. That's what Writers is all about.
- Publishing books. That's also covered by Writers.
- Managing books. The proposed Libraries is about professional book management.
- Trading and collecting books.
- Reading books.
Judging by the example on-topic questions on the Books proposal, the intended audience is firmly readers. I very much agree that Literature would be a far better name for that.
If there is interest in a separate site for book trading and collecting, it should come as a separate proposal. The professionals there would be booksellers, not literature professors.
I very much disagree that the overlap with Science Fiction and Fantasy is an issue. There's an SF community, with plenty of people who read SF books and watch SF movies and series and so on, but don't necessarily care about other genres. There's a literature community, with plenty of people who'll read any genre, but don't care for movies. It's natural that each community would have its site, and questions about written SF would be on-topic on both sites (with different expected skew in answers).
There are precedents on Stack Exchange of sites with significant overlap. For example Ask Different is about all things Apple, and there's also a site about Unix & Linux. Many questions about Mac OS X, which is a unix variant under the hood and visibly an Apple product, could end up on both. In practice, AD mostly gets the GUI questions and U&L mostly gets the command-line questions. And there's an Ubuntu site, which is technically a sub-topic of Unix & Linux; yet both sites are working well, and the occasional migration isn't killing us.
One thing that worries me about the book proposal is that three of the example questions are book recommendations. We tried that on SF&F, and after a while we weren't so hot about them, because most recommendation questions were pretty bad (the questions were usually too broad, and the answers weren't very useful because they rarely explained why the answerer thought the proposed book was a good fit).
Before that, Gaming had issues with recommendations and ended up rejecting them. It's a trend.
Therefore, rather than just renaming Books and going with the existing definition and commitments, I recommend resurrecting or recreating a Literature proposal, and referring people interested in (reading) books to that (instead of the opposite.