Digital video cameras aren't all that different from digital still cameras. They just string a series of still shots in sequence.

Used to be a pretty common aproach to use a minimum shutter speed of 1/60 sec for still studio work to eliminate decernable motion blur with an 85mm lens. Wide angle lenses could get away with maybe 1/15 sec, but we're talking minimum motion in the subject material.

If the subject matter moves to any serious extent, even at 1/15 sec a wide angle lens will show it in a single frame. And a movie taken at 15 fps is just a sequence repeating that problem, regardless of the kind of shutter used to record it. Last time I checked, the latest GoPros are up to 60fps.

If you complicate that further with an autofocus feature that tries to refocus everytime anything in the frame moves - good luck getting anything worth looking at at all.