There is no non-social use case for Nostr because Nostr is a protocol for social interactions.
Discussion
Nostr powered commerce! A lightning powered eBay. Some attempts already but they tell short.
I have one: permissionless data sharing between online applications.
An example:
An online course with user inputs, a second app such as DVM that does some AI processing on it, a third that organizes the new content into a usable format for presentation or publication. Devs for the three apps don't need to know each other, the user does no download-uploading or copy-pasting, and the content can be encrypted so the user must be involved for the data transfers to be made and the user maintains ownership.