Presumably the filmmakers know they have a huge, built-in audience if they stay close to the books. They must also know that this audience will savage the films if they deviate too far. PJ started well but, by the time he was done with The Hobbit, he had turned his films into comic book/video-game style adaptations for twelve year olds. The smart course for Amazon would be to bring artistic discipline back into the mix and do a faithful adaptation. Of course, smart and Hollywood are not always a natural mix.
From my limited understanding of this Amazon series, I’m not sure it’s possible to “stay close to the books. The plan from what I’ve read is to flesh out the back story, i.e., the sort of stuff that appears in the appendices of Return of the King. Tolkien’s style in those sections is basically “summary.” Sure, there are character names of various kings, etc. but they’re not well-developed characters. The plot points are painted in very broad strokes much like “Chronicles” in the Old Testament. If you made a TV series about some of the obscure kings in Chronicles, there’d be a lot of room for “not staying close to the book” because, well, we’re talking about turning, say, 20 sentences of prose into 3 hours of television.