There are two main reasons for this.
First, we have to realize that writing does not really have “overwhelming value” for everyone. Writing is hard to develop. If you do not have a real need for it, it does you no good. The only societies that really need writing are those that have merchants and governments and therefore need to have things like records of who owns what.
Second, it is very hard to develop writing and so most societies only get writing by borrowing it. As Diamond says (on p. 237 of the paperback edition of the book)
…the vast majority of societies with writing acquired it by borrowing it from neighbors or by being inspired by them to develop it, rather than by independently inventing it themselves.
The significance of this is that people who live near to other people who have writing have an advantage. But many peoples did not live close to literate societies. As Diamond says (again on p. 237)
Had they been located nearer to Sumer, Mexico, and China, they might instead have acquired writing or the idea of writing from those centers…
This means that there are two main reasons why a people would not develop writing. It might not have been useful to them and/or they might have lived too far from literate peoples to be able to borrow writing systems.