It sounds like you're talking about multithreading in general rather than async specifically. If you don't need multithreading then you don't need async... that's not too surprising.

I write an application that previously wasn't using threading to avoid blocking the UI. Certain long-running tasks would freeze the app for some time. It's not a big deal since it's an internal app for my work team, but now that the async syntax and semantics are a bit easier, I've started using them and my app is more responsive.

Async doesn't do anything fundamentally new. If you already implemented multithreading in your application that you're happy with, there's no compelling reason to switch to doing it the async way. But for new development it seems like it should be the default.