Originally posted by Gimbal On the other hand, a light touch of noise reduction might get you the same result.
Not really (sorry), the foreground is a dark portion of the frame, the clouds are bright, clouds areas that move will be replaced by a single frame, noise is minimized in bright areas anyway. The foreground is fixed, this is were the 4 frames are combined, reducing noise without reducing detail in the shadows. So, it's not like noise reduction will produce the same result.
---------- Post added 19-03-19 at 12:32 ----------
There is a way to benefit from pixel shift even in scene containing moving parts, it is counter intuitive, it is long exposure (such as 5 to 10 sec.). Using a ND filter for extended exposure time makes moving parts of an image blurred while other parts aren't affected. When the 4 pixel shifted frames are assembled, the blurred parts are more clearly defined as non-pixel-shift areas, on any smoothed part it is also easy to remove residual artifacts if any. The fixed parts of the frame are demoisaiced with combining 4 frames benefit from lower noise and eventual higher resolution when not limited by the lens / aperture diffraction. Long exposure is a method that allow using pixel shift again when some parts of the frame are moving.