None of the answers so far seem to be answering the actual premise of the question.
>What’s stopping them from just having red, green, and blue pixels, and then just making those go as bright (and as dark) as possible?
In short, the thing stopping us is we cannot make red pixels that are perfectly the outer-limit of what is red, and green pixels that are perfectly the outer-limit of what is green.
Longer answer: you’ve probably seen a color space chart ([CIE 1931 color space – Wikipedia](https://en.wikipedia.org/wiki/CIE_1931_color_space)), which maps all the colors of the visible spectrum (the full color gamut). Along the chart are usually numbers that correspond to the wavelengths of all visible colors from about 380nm to about 750nm.
By taking a red, green, and blue pixel and plotting them on that chart and connecting them with lines to make a triangle, all the colors you can make by mixing those pixels and adjusting their brightnesses would be inside that triangle.
Thus, the more of that chart the triangle fills, the more colors you can make by mixing your pixels. However, if your red pixel is not totally red, but more orangeish, there is no amount of mixing you can do to make it redder. As you can see, to maximize how much of the color space you can make, you need that triangle to be as big as possible, which means you need to make red, green, and blue pixels on the very outer limits of what is red, green, and blue. More specifically, the perfect red pixel would emit only ~650nm, the perfect green pixel would emit only ~520nm, and the perfect blue pixel would emit only ~450nm. If we could do that, then our TVs and monitors would be able to show *most* of the colors in the colorspace no problem.
The good news is we can make nearly perfect blue LEDs. That part is (relatively) easy. Red and green are tricky. We can’t make anything cheaply and effectively that emits only those perfect red and green wavelengths. That’s why, right now, consumer TVs and monitors can’t display all the visible colors.
With LEDs, typically we use various phosphors or quantum dots to “convert” blue wavelengths to another color wavelength. But the conversations are not perfect. Each method of “converting” has benefits and drawbacks, and none of them produce only the perfect reds and greens that we need. For example, some methods produce a wide range of wavelengths, which requires us to filter the unwanted ones and thereby sacrifice brightness. Some methods produce a wavelength close to but not ideally where we want it. But if someone invents the perfect red and green LEDs, then we would in theory be able to show all (or nearly all) the visible colors.
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