Pardon my ignorance but wouldn't LCD need polarized light to perform the darkening? Maybe a transparent pixelated electrochromic display layer might work
The backlight of an LCD isn't itself polarized. A TN LCD display is made of two orthogonal polarization filters with the liquid crystals in between. In their relaxed (twisted) state, the crystals rotate the polarization of the light so that it can pass the second filter. When a voltage is applied, the crystals straighten and the second filter blocks the light.
LCD usually has polarization filters already glued to the back