The main use case if for seldom used APIs. If I run a service where the API isn't used often, but I need it quick when it is, Lambdas or something like it are perfect.
As it turns out, a lot of APIs for phone apps fit this category. You don't want a machine sitting around idle 99% of the time to answer those API calls.
If you rarely need an API but set something up like this just to rarely use it, it seems one needs to write their own code for this functionality and not go through hoops to run someone else's. That just sounds so bizarre.
Not someone else's API, your own. You make an app. It needs an API that you create (perhaps to sync up scores or something). You don't want to run a machine full time just to accept one score update a day.
As it turns out, a lot of APIs for phone apps fit this category. You don't want a machine sitting around idle 99% of the time to answer those API calls.