To see why a centralized government is useful, look at Diamond's description of the Fayu at the start of the chapter or look at the biography of the Iyau woman on p. 277 in the paperback edition. In both of those passages, we see that societies without centralized government have a hard time providing their people with stable lives.
As societies grow larger, they need governments. They can no longer be held together by family ties. Someone needs to have the authority to do things like preventing people from killing one another. This is where government comes in. Government strengthens societies by creating ways for large populations to live together in peace.
Of course, there are problems that go along with having a centralized government. However, a society without such a government, like that of the Fayu, is one that is very unpleasant and dangerous to live in.