Keeping old newspapers is never a bad idea. I always have a stack for when I want to use them if I am spray painting or for cleaning windows. This is an article that lists 36 uses of old newspapers some of which I would have never thought of, for example:
Adding moderate amounts of wet, shredded newspaper to a compost heap makes good compost material and “gives earthworms a tasty treat.”
Covering flower beds with newspaper and soaking them with water. Then covering the paper with mulch will smother weeds and kill them.
Discover more uses for old newspapers in the link below: