The uses for APIs that don't return data seem pretty limited in our realm (SaaS). One example is handling incoming notifications/webhooks from other systems. By their nature these are asynchronous and the caller (the external system) does not usually expect a meaningful response, so for sure we can use SQS to buffer the incoming API calls.
But for the APIs that we offer, virtually all of them have an online response. In my experience this is not an unusual pattern (for SaaS APIs anyway).
I feel that these technologies are somewhat biased towards super scale systems that are highly decoupled and asynchronous - perhaps the sort of systems that Amazon are used to dealing with in-house - rather than simple old business systems.