There have been LCDs with subpixels beyond RGB, notably Sharp’s Quattron which added yellow. Single-chip DLP projectors all use multicolor filter wheels, including very high end ones.
I'm going to have to agree with BrianHG on this one. White channels are a clever workaround to make up for deficiencies at the expense of picture quality. Pure RGB direct emission is the way to go.
Sharp’s Quattron was a short lived product. High brightness business grade portable DLP projectors need white on the filter wheel, but high end home theatre DLPs have moved to RGB LEDs or laser light sources. To achieve the highest brightness and picture quality, movie theatre DLPs have three DLP chips and RGB lasers.
A white channel reduces the colour gamut at high picture levels. Imagine that the white, red, green and blue channels can reach 60% of the desired maximum brightness. Typical medium brightness colours would be perfect, even if you use as much white as possible. But what happens if you need pure red 75%,0%,0% ? You need to compromise the picture quality in some way. You can either reduce the colour purity or dim the pixel below the desired brightness. That would be either 15%W,60%R,0%,0% or 0%W,60%R,0%,0%.
From what I've read, LG WOLED TVs have significant image processing behind the scenes. There is a very aggressive automatic brightness limiter because of a strict power budget for the whole panel. This means that a full screen of pure white is very dim compared to pure white box in the middle of normal image.