> What happens when we aren't needed?

Depends on the political system. Under socialism authority will simply improve the environment by reducing your carbon footprint with eight grams of lead. Under capitalism you're already not needed to anybody.

> Why would it get any better when AGI can do everything humans can do?

Because that "better" we are building ourselves with our own hands. How it can get worse? Only if authority forbid us from building ourselves like we always did and decide to improve the environment.