But it will be better if the min shutter speed can be set automatically as a multiple of the lens focal length.
What's the logic, there? Are you saying you want to pick the multiple, e.g. 1 / (2x focal length) or 1 / (4x shutter speed)? What about IS lenses - should the camera then know if a lens has IS, if it's on or off, and if on drop the setting by the rated stops of stabilization?
Actually, the camera already defaults to 1 / focal length in Av mode on FF bodies, and 1 / (1.6 x focal length) on APS-C bodies, ignoring IS. But, if you specify a min shutter speed, your setting overrides that. For example, if I set 1/250 s and mount a 600mm lens, even in good light it will select 1/250 s or 1/320 s. But with min shutter set to Auto, it will use 1/640 s if there's enough light.
For me, the utility of the min shutter speed setting isn't to prevent camera shake - Auto already does that based on the 1 / focal length rule. Rather, it's to prevent subject motion from blurring the shot. With a 24-105mm lens, at the long end it will select 1/100 s in Auto, which is ok, but at the wide and it will select 1/25 s and there will often be blur from involuntary or small subject movements. I set a min shutter of 1/125 s for 'still' people, 1/250 if I expect them to be moving (not sports, just moving around), and for wildlife/sports a min shutter of 1/500 s (which is possible on the 1D X using the shutter speed range setting, but not on the 5DIII).