Absolutely agreed.
Though you mention that walking is what helps you keep distractions under control, I like to go walking while listening to history/science podcasts, since it helps me understand the content a lot better.
The act of walking is said to be greatly beneficial for thinking in its own right [0].
So when I get an idea, I usually drop everything I'm doing and go for walk. And my anecdata can only confirm that it's beneficial.
This is why I am so excited about the idea of working remotely using AR glasses. Just imagine going hiking through the mountains while checking your emails or being on a conference call – only taking breaks to type out some code on a portable keyboard.
Regardless of the cognitive performance boost this would give you, it would also mitigate a lot of the health issues we humans have started accumulating since we started sitting down all day.
Of course Einstein also famously claimed to have only moved to Princeton for the walks home with Gödel [1].
[0] I found this news item in a pinch, but I'm sure there are many studies to substantiate the claim: https://news.stanford.edu/2014/04/24/walking-vs-sitting-0424...
[1] I would have to do some digging to find the original phrasing (Einstein is often misattributted), so take it with a pinch of salt. But there is an entire book who's title alludes to this :
https://en.wikipedia.org/wiki/When_Einstein_Walked_with_G%C3...
(the book is great btw)