> Humans don't require input to, say, decide to go for a walk.

Impossible to falsify since humans are continuously receiving inputs from both external and internal sensors.

> What's missing in the LLM is volition.

What's missing is embodiment, or, at least, a continuous loop feeding a wide variety of inputs about the state of world. Given that, and info about of set of tools by which it can act in the world, I have no doubt that current LLMs would exhibit some kind (possibly not desirable or coherent, from a human POV, at least without a whole lot of prompt engineering) of volitional-seeming action.