Upvote:7
Through the musket era, formed troops prevailed through achieving higher rates of fire. With rates exceeding 4 shots per minute for Wellington's Peninsular veterans, and claimed to approach 6 shots per minute for Frederick's Prussian Guards, a rate of 2 per minute (as in the video) is horrendously bad for formed infantry. Likewise it seems clear that the running pace is slowed by the reloading effort. And formed troops cannot run at speed or for more than a few seconds without loosing cohesion.
The questions then becomes: Under what circumstances is it desired to reload while running, with a significantly reduced rate of fire? I believe that the only such circumstance is as described for the Virginia borderer in the question. When badly outnumbered and small in number, so that slowing will result in becoming surrounded, it is imperative to keep moving. Note that the anecdote mentions the chase lasting over several miles, so a steady jog as in the video is quite fast enough. Only in this circumstance can I see value in reloading while running. Such a circumstance would have been much more common along the Appalachian frontier than anywhere on a 18th or 19th century European battlefield.