[shiro]

I'm not sure what source you derive from about the particularity of "sitting still". You imply that not being distracted from the given task? Or the physicality of sitting still has the benefit? (The two can be distinguished easily---if the latter is the case, "sitting still without doing anything, and just daydreaming wildly" would also have benefit.) Or you mean meditation? That's a different activity at all.

In the ADHD case, it seems about the way of processing stimuli. They (or at least my kid) need a sort of synchronization stimulus (or, outside distrubance, in the way that disturbance suppresses the divergence of hypersensitive systems) to keep his mind on rail. If no such stream of stimuli is provided, he must create one by his own. I try to make him find and build his own toolset to work with. (One of the activities, for example, is tapping along metronome while doing other tasks.)

[Edit] I see your comment in other thread that you refer to Zen meditation. I've learned meditation and I agree on its benefits, but it can't be applied to the current discussion of school setting---"sitting still listening lectures" and "sitting still meditating" are very different activities. The latter would certainly develop the ability of the former, but I'm dubious about just forcing the former.