Has such a thing been considered? Can it be done? Would it be useful? Has it already been done?
The answer, I believe, would be YES | YES | Not really | YES.
You can search for Sharp AQUOS Quattron - LCD TV. It has an additional yellow channel so it is basically a four-channel display. Yet as you see, it was 14 years ago and the market had... limited excitement about it.
If you consider the problem mathematically: the human perception for color can be almost perfectly decomposed into 3 different components (R, G, B), then it would mean that the space can be represented by these linearly independent (with a slight abuse of notation) components. They are just like 3 orthogonal vectors that can perfectly represent the 3D space. So why bother adding another linearly dependent component (like yellow)? There are few more things to consider:
- Compression algorithm for 4-(or more)-channel video, how to you encode and decode it? Will the loss after these operations be acceptable (since, the additional channels are linearly dependent, compression might just... annihilate possible gain in visual quality)
- Graphics related algorithm: RGB rules them all... let's sell our product to those manufacturers and convince them to support our new display protocol.
- Hardware design for your display. This is obvious.
- The quality improvement might just be hardly perceivable. It might be like when your wife takes two similar lipsticks and asks you to distinguish between one another...