I never thought that the case for patents was to increase productivity. I always thought that their purpose was to eliminate trade secrets: people are going to invent stuff whether you want to or not, but without patents, they'll take the secrets to the grave. My favourite patent of all time is Michael Jackson's smooth criminal patent: https://mashable.com/2015/03/28/michael-jackson-shoe-patent/... This is the patent…
I suppose one benefit of patents is to reduce incentives for corporate espianage.