> In those cases, it can be a "free lunch" in the sense that the curiosity-seeking mind got fed while whatever physical task that needed to get done also got done with less procrastination and dread.

The interesting thing is, exercise is more effective and beneficial when brain is focused on what body is doing, i.e. doing mindful exercise is more beneficial than giving brain a pacifier while body is doing something else.

On the "procrastination & dread": The brain has a daily limit on hard concentration. From my personal experience (during my Ph.D.) it tops around four hours most. I also find staying put very useful and beneficial, because after stuffing too much information into it, your brain needs to sift through and filter it. Also I find myself refining my previous ideas while staying put and doing nothing maybe except writing down what I'm refining or journaling.

You can create brain fatigue, fog or plain burnout by trying to make it run flat our all day long. Let it rest, reset and restore. You'll have much more happier.