Humans also frequently need to try a wrong approach first to get the idea of a better approach, no matter if we're rested or not. Which is why it's important to be able to throw away prototypes rather than push an "it seemed like a good idea at the time" to prod.

But having a good sleep, walk in a park, shower, etc lets us think better than if we're just banging our heads in the same corner all day long. Breaks are important. General health, too.