I haven't found git to work much differently in practice, at least with papers (I haven't written a book in it). You will end up with way too many conflicts unless you basically "lock" sections through either a software mechanism or agreement, because edits often touch or reorder many paragraphs. A copyediting/wording pass will typically touch every paragraph, for example, and these are more frequent in writing than refactoring or variable-renaming passes are in coding.

You can somewhat improve the situation if you adopt a somewhat weird source-formatting policy, where you write each sentence on one separate long-ish line, rather than flowing by paragraph. Then you will be able to automatically merge as long as nobody has made an edit or move that touches the same sentence, giving you better merge granularity. But even then conflicts happen pretty often, and few people like this style of formatting (maybe it'd work better with tool support).

For a book this might work better, though, because I assume you'd be making less frequent edits, and people would less often be working at the same time.