Anyone who writes their own, not freely available, manual to a free software program, is dividing the world into two halves: Those readers who can afford this new book, and will pay the author (not the writers of the software, mind you) for a nice manual, and those readers who can’t afford to pay for this new manual, and will have to do with the inferior¹ official manual. Those readers who can afford the new manual will not be incentivised to improve the official manual, since they have the new, better, one. Therefore, this act (of creating new manuals which are not freely available) is reducing the number of readers who can be expected to help improve the official manual to those readers who cannot afford the new manual. These effects, i.e. reduced funding and reduced help to the original software authors, is not, to me, worth it to have a new, even if better, manual.
① Presumably, by their own standards, since they wrote a replacement manual.