I would invite you to experiment a bit and to answer your question yourself.
But yes, I can think in several cases where you should shot at higher framerate where this motion blur is actually a problem.
The first case is the one you describe. The camera shake will produce blur on directions we do not want.
Another case is time-lapse. You can have objects ...
It just refers to the shuttet speed and FPS.
As you probably know, 360° means the entire time, the frame is exposed.
0° means it is never exposed, 180° half of the time.
With digital shutters you can just take your FPS, for example 24, and calculate the corresponding value.
For 180°, you can double it 24*2=48 so youbget a shutter speed of 1/48s.
For 360° ...
I don't know where they have "TV motion" from as at least in my area we use 1/(2×fps) for TV too. Or higher for sports.
1/(2×fps) simply has a "natural" motion blur to it which is often used in cinema as it is often the best choise.
A shutter slower than that has much more shutter, I describe it as dream like.
A shutter faster than that often looks like a ...