It reminds me of the LCDs on digital cameras, some of which use the same trick to reduce costs --- natural photos don't look any different, which is why it gets a pass, but text has a noticeable graininess to it as a result.
They can! Not frequently, I'll grant. Once I was using Lightroom and was very confused by a pixelated looking edge of a yellow flower against a blue sky, the edge of which moved diagonally across the pixels. Eventually I realized it was the mosaicing! I actually ended up switching to RawTherapee for that picture, the AMaZE demosaicing algorithm handled it much better in that particular case. Lightroom in the last few years added a high quality demosaicing mode that you can selectively enable, and it handles the picture correctly. It's pretty slow though.
In any case, reporting resolution using the single-color "pixels" is probably more justified for an image sensor (with its array of square light detecting sensors), than it is for an LCD screen, which is usually a square array of non-square sub-pixels.
When we apply that work to screens, our eyes can't really post-process and correct for these errors.