The key question is: while said REST call is happening, what is the caller doing? Normally, he's sitting there and blocking his thread until the call finishes (i.e. consuming one thread from the connection thread pool). With async/await, the thread is released back into the thread pool until the result is ready, then it picks up where it left off.
So anything where you might want to deal with background operations that take a long time (including network / db / filesystem access, i.e. most applications that aren't pure functions) in a connection-oriented system can greatly benefit from async/await. Even if it's just a regular desktop app, it appears to be a useful mechanism for coordinating different background tasks.
The nice thing about async vs. typical closures is that it neatly avoids a lot of nested scopes.
It is pretty simple for that scenario and avoids the cross thread marshalling you need to do in win forms.