Some JVC projectors have an "e-shift" function that rapidly moves the image up and across half a pixel in each direction, repeating every frame, eleminating the "screen door" effect altogether. It almost works as a kinda psuedo-4K but with a regular 1080p panel.
I agree with Harmy that 4K content in the home is a waste and that there are other, far more important factors to consider than mere resolution.
I am watching on a 130" screen, by the way. The pixel structure on my 1080p LCD projector is not visible at normal viewing distance.
I think this "e-shift" technology and the like sounds like a smart alternative to bumping up the res, which will create more problems.