John
You mentioned you are only focused on one book, so some/much of the following only really applies if you expect to do more of this type of work. I produce about 45 books for education ranging from 3 to 20 chapters, and Mike has summarised the key benefits as I would see them too – in particular the management of styles/colours both within a book but also across books.
I would also add a couple more things: reordering chapters is trivially easy by dragging in the book pane; managing situations where you want a fixed number of pages in a chapter is just easier because you can switch off Smart Reflow and work on that chapter alone to fit the content; the text frames in each chapter are easily threaded together via the master page setting and end with each chapter so particularly as the book gets towards proof stage you are less likely to change pagination/have overset text as final edits are made; working with smaller files feels better, whether your system is fast or not; if edits need to be made to a chapter it can be worked on separately and then use Replace Document to slot it in – if you have more than one editor and/or use some kind of version control this is very useful; section page numbering schemes are just a bit easier to manage; and if you have reused content between books then you can have the same chapter file appear in multiple books so you only have to edit in one place. Note that things like find/replace and spell check can still be done on the whole book in one go, but you have to have all the files open and select All Documents in the Search dropdown. Also, if your source material comes from Word, then I would _definitely_ be encouraging my author to have separate chapter files because 300-page Word documents can be a nightmare!
A couple of gripes about working with book files: you still can’t dock the book panel and save it in a workspace, it always comes back as a floating panel and easily hidden behind the application window or on the wrong monitor; if your printer wants you to conform to a page multiple, Preflight can check this but only at a chapter and not a book level, i.e. it doesn’t work; if you use cross-references, Indesign isn’t clever enough to automatically offer the chapter files in the Document dropdown selector, you still have to open them individually from the file dialog.
Even if none of the above really applies, then I would highlight another of Mike’s points, which is file corruption. The number one cause of crashes for me is when Indesign has to reflow text and for whatever reason it just doesn’t like it and boom (repeatable after each recovery with the same edit). Longer documents have more complex reflows. Doing a round-trip via an IDML document to try to clear out whatever invisible cruft is causing the problem is easier when it’s a shorter file and the rest of the book is not affected.
Nick