You use async/await when you are doing any sort of IO in an application that needs to be responsive. Example: your ASP.NET thread pool is starved because all your request threads are waiting on IO. It's useless to have those threads waiting there for IO when they could be processing other requests to your server.
You're obviously going to see some overhead from the state machines generated, but that's negligible compared to the gains you'll see in throughput and code readability(compared to the older ways of doing async code).
The same reasoning extends to UWP, don't block your main thread with IO so it can still process input. Obviously there's other ways to handle async in a desktop app, but async/await just make it so much easier to reason about your async code. It looks exactly like you're writing synchronous code.