A basic example is some compute service, say image transformation. You just run computations where all the input is in the request, and all the output goes to the response.
I feel like you still need to the DB for that, for auth at a minimum (which might not need to hit your main DB I guess) if not for logging (spend credit/record usage/just analytics). I guess all of that could be skipped with something like a JWT and log ETL process.
I'm intrigued by edge computing but the DB always seems like the bottleneck so thank you for the example.