CMY/RGB is not an arbitrary choice for color model. It's the best approximation for stimulating the color receptors in the human eye. RYB on the other hand is just historical model that still exists because traditions in the art teaching change slowly.

It's a wrong notion of primary colors that one could choose any three colors for primaries. Yes, it's possible to choose any three colors and mix a set of other colors within the triangle defined by these three. However, by definition a primary color is a color that can't be mixed from any other colors. Cyan, magenta and yellow are such colors. It's not possible to mix cyan or magenta from the RYB palette, on the other hand red can be mixed from magenta and yellow, and blue can be mixed from cyan and magenta.

The reason why RGB/CMY are the primaries is exactly because of the stimulus response of the human eye. The purpose of color reproduction is to cause a specific response in the three receptors in the eye. Since there are only three different kinds of receptors, it's possible to produce the exact same response in the receptors in multiple ways (thus we have metamerism). RGB primaries are chosen because each of the primary colors causes a large response in one type of receptors and as small response as possible on the other two receptors. (And CMY is then the opposite of this by causing as large response as possible on two receptors, and as small as possible on one.)

The reason why the traditional RYB palette has two versions of each of its "primaries" is because RYB "primaries" are so bad at covering the visible color gamut that by introducing two versions of each color it's possible to expand the triangle from which to mix into a hexagon.

The exact wavelength profiles for R, G and B may vary between different display technologies, and some technologies can represent the color better than others. This doesn't mean that the RGB model is arbitrary in any way, but that there are just practical reasons why the theoretical optimum is not always reachable. Some of the standards for RGB reproduction take this into account and define a color space that follows the common technologies rather than the theoretical optimum, and thus have a limited gamut.

Color printers with more than 4 inks don't abandon CMYK model. I have a large-format printer that in addition to basic CMYK has gray, light cyan, light magenta and light yellow inks. The purpose of these lighter shades is to allow printing light areas with less visible dot raster. The color model is still CMYK.

Some printers also include red, green and blue. These exist basically for the same reason there's black in CMYK. Even if CMY is theoretically correct model for wavelength response to match the human eye, there are real-world limits to ink and paper technology; for instance 100% fill of all CMY is not as black as 100% fill of black.

Purpose of spot colors is not related to color model, but color reproduction. If you define your spot colors by Pantone number, there's a guarantee that the color will match exactly what you ordered. It's much harder to get exact color reproduction with CMYK process, because the number of variables affecting the end result is so high. Another purpose for spot colors is all kinds of specialty inks like metallic colors etc. Sometimes it's also a cost issue, because it can be cheaper to use black + one accent spot color than a full CMYK process, or a quality issue, because with spot colors you don't get the color raster.