interesting how these things always get so heated! us boys with our toys
here's my take on pixel shift from some brief experience with it.
in order to really resolve a lot more detail, the pixels have to be smaller. shifting larger pixels around does have some effect since the pixel isn't a perfect field of light-gathering goodness, and fine details which otherwise would have disappeared are captured.
a better application in my opinion, as michael suggests, for pixel shift should would be using the shift on still subjects to simulate a "true" rgb sensor. the shifting actually moves a red pixel onto a green pixel and then a blue pixel onto the red pixel. this is like the old color wheel sensors. great for still subjects, useless for anything else.
since each final pixel in a bayer-interpolated image is in fact the result of data from adjacent pixels, we already have a bit of the same problem that the "shifting larger pixels" approach entails. our 45.7mp d850 images aren't really quite that good, which is evident when compared on a pixel by pixel basis to a "true" color image.
it's interesting technology. not too interesting to me since my shooting needs vary widely and often include movement. for still subjects with a still camera, it's definitely good for a bit of a bump in apparent "resolution." what we really need is a device which records the wavelength and intensity of light at each pixel.
imagine that!