I think this idea has been echoed multiple time in history. For example, the Peripatetic school[1] (in ancient Greece) etimologic roots is in "walking" or "the pleasure of walking". Some rumors say that it is by walking that thinkers could achieve correct or deeper thinking.
Apparently, a lot more philosophers have a very deep relationship with walking. Nietzsche and Kant both spent hours walking to think[2].
I think inherently, we are not souls, we are not brains without a body. When we do something, our entirety gets to work, and sitting all day in front of a screen is no way to think or live.
The benefit is like rubber-duck debugging. For about 45 minutes I have no interesting things to distract my mind and I automatically start thrashing any meaty problems I left specifically for this. Works for me.