Depends where you're walking how free your mind is to wander - if you're walking through woodlands, on rough tracks, in country with wild animals then you could have no cognitive overhead available for pondering.

I walk, pandemic aside, 45mins each way to work as it's on quiet pavements I can walk without thinking which is a different experience to walking in rough country when one needs to focus on the walking itself.

For me I come up with a couple of inventions/innovations every week (ideas are cheap as everyone says, which is rubbish for me as ideas are about my only differentiator) but unfortunately I don't have facilities or time (nor probably the skills) to develop them.