There are two completely separate things being discussed: frame rate, and shutter speed.
Low frame rates like 24 fps produce "judder" which shows up as annoying double-images when the camera pans horizontally.
High shutter speeds produce a different sort of annoying artifact, although sometimes the same language is used to describe it as is used to describe what happens when filming at frame rates that are lower than the persistence of vision threshhold. The shutter speed artifacts are more subtle and generally not as annoying as those produced by the low 24 fps frame rate. You don't usually notice them when the camera pans, but instead they become more prominent when some object moves quickly through the frame, such as you seen during most sports.
Most people can acclimate to watching video taken at high shutter speeds, but it is pretty difficult to get used to watching the judder from low frame rates.
However, if the camera doesn't move, low frame rates can be quite watchable. Here is some ancient movie film I transferred and restored. It is from 1928 and was taken at about 12 fps with a hand-cranked camera.
You can eliminate judder by synthesizing additional frames, using motion estimation software. If used with motion stabilization, the result can be quite smooth, although the process does introduce artifacts that can, under certain circumstances, be quite annoying.
Here is some 16 fps film that I modified to 30 fps: