If you're getting started with LLMs, the first step is an API call to OpenAI (or some other foundational model) to get a feel for it, then think about how you want to integrate with your application. Burr can help standardize the structure, allowing you to think less about it at any given point (as logic is encapsulated into actions). Furthermore, the UI can help you debug.
With a few POCs at your company (assuming you want to iterate and get into production), Burr can help abstract some complex parts away (state management and telemetry), and make your code cleaner and more extensible, which can help you iterate quickly and explain what you're doing (you can always draw a picture of your app).
We think that it buys companies something they really want -- the ability to swap out implementations/vendors as it decouples the logic from application concerns.
So, if you have logic that's starting to get complicated (and might get more-so), I think Burr is good. If all you're doing is a single wrapper over a GPT-call, it might be overkill (or not! things tend to grow in complexity).