I seem to recall studies in controlled environments where people were not allowed to exercise, and there was a significant difference in calorie burn attributable to small movements. So the homeostasis argument seems totally plausible to me.

I think it's more about the level of background "noise" in the brains of young kids. When unchecked/unfiltered in some kids it will start to trickle into the motor/cognitive areas of the brain and that's how you get fidgeting, twitchiness, those kinds of things.

Balancing on an exercise ball seems to engage those involuntary areas while not interfering with high-level processing.