When I think of serverless I think of an application that runs on the desktop, in the browser, or WASM. The generated data is stored in the same place the application is run. The only distribution is the initial delivery of the application. Not only is that confined to one side of a network no network is required.

I suppose the reason I have trouble accepting this use of serverless is in the case of a connection interruption. If the connection goes down the application is killed, which sounds like a service availability failure to me.