I can't speak to nook, but for Google Play and Kindle the books are saddled with DRM. That doesn't mean you can't read them, it just means that you can't (easily) just copy/paste them to your computer from the N7. You can read Google Play books through a web browser at play.google.com. And I believe something similar exists for Kindle.
The advantage of these services is that they will sync your place in the book, bookmarks, notes, etc. For example I can read a chapter or two of a book on my android phone with a Google Play book while I'm standing in a line or having lunch at work or something similar, and then go home and pick up my Nexus 7 and it automagically goes to the place I left off reading on my phone. It'll do that in the web browser as well.
EDIT: as for books you've already read. They show up on in the apps because they exist as a purchase history. I know that on play books you can tap and hold on the book and select remove from Library, however that will mean you can never re-download that book and read it again.
Really the books actually don't live on your device after you've read them (unless they're "pinned" on play books). the list you see is just a listing of your purchase history, much like having a bookshelf full of books.