The selection of 24p/25p/30p/50i/60i/... involves device-specific compromises that may or may not work better for a given scene and a given artistic intent. In other words, simplified, general theoretical approaches may not give satisfying answers.
This sounds very true to me, although I have little experience shooting video.
My Panasonic plasma TV has a 'sub-sampling' refresh rate of 600Hz which, it is claimed, reduces the blur in fast action. The figure of 600 presumably has been chosen because it is the lowest figure that is divisible by all the current video frame rates, 24, 25, 30, 50 & 60fps.
As I vaguely understand, but I'm not at all certain, when the video source or broadcast is 50i, for example, the TV processors may first combine each pair of interlaced frames recorded at a rate of 50 fps to make 25 progressive frames per second.
On the other hand, during fast action, combining two frames 1/50th second apart would produce a very blurry progressive image, so maybe the TV processors simply interpolate to fill in the missing lines to produce 50 fps progressive.
Each of those 25 progressive frames per second will then be displayed 600/25=24 times, or 12x in the case of 50 fps progressive, to produce a totally seamles and totally jerk-free result.
On such a display with a 600Hz refresh rate, I have difficulty understanding how using a fast shutter speed to shoot the video would produce any sense of jerkyness.
Unfortunately, I can't test this for myself at present because I am currently travelling. My video camera is the Nikon D7000, and so far I've shot all video at 24fps in aperture priority mode, setting an ISO that seemed roughly appropriate for the lighting conditions, and allowing the camera to choose the shutter speed.
I think it might be time to start experimenting with different manual shutter speeds. So far the only obvious trouble I've had relates to sound. I've been using the Sennheiser MKE 400 external microphone which fits into the D7000 hot-shoe. On one occasion, recording a cultural show in a restaurant in Pokhara, with camera fixed to gorilla pod on table, I was certain I had pressed the record button firmly, then continued eating my meal and watching the show instead of peering at the LiveView screen.
A while later, at the end of the routine, putting on my glasses to stop the video and review the result, I discovered I hadn't recorded anything. When the next song and dance routine began, I paid special attention to make sure the red record sign was active after pressing the record button, but I couldn't get the camera to record.
My memory card wasn't full. Had this Made-in-Thailand camera become faulty? I had already experienced an inability of the camera to autofocus in cold weather, not excessive cold, just normally cold around the freezing point. It was frustrating having to manually focus everything in the early mornings along the trail to the Annapurna Base Camp, until the camera warmed up in the sun.
Anyway, after searching the menu for microphone settings, suspecting the sheer loudness of the sound coming through the restaurant's loudspeakers might have something to do with the problem, I solved the problem by setting the mic to 'low sensitivity'.