As an artist I have a perspective on color from a pragmatic (as opposed to theoretical) point of view. Visual artists use materials like paints or inks applied to substrates. These all are exploiting subtractive color, primaries are complements of additive color, CMY vs. RGB.
The standard color wheel interleaves CMY with RGB, which sets up useful symmetries and complementary relationships. But of course, the color wheel is really a color cylinder, or set of cylinders when color properties other than hue are considered. Color saturation and value are crucial to artistic work, but when these additional dimensions are accounted for it's no longer the simple model the basic color wheel portrays.
Color classification systems emerged in the 20th century and over time evolved into the highly rigorous regimes codified by the International Color Consortium. Everybody is familiar with ICC profiles and their uses. I can't say I have a thorough understanding of them, I'd guess relatively few people do.
Artists don't have handy ICC profiles to guide creating a painting or print. They learn how to mix colors mainly by trial and error. However the paints and inks are precisely formulated by manufacturers who very much understand the science of color. This precision results in product constancy which makes life far easier for artists. With experience they gain an intuitive "fix" on particular colors and their locations on the extended color wheel.
To make it even more convoluted there are metallics, gold, silver, copper, etc. and the range of man-made iridescent and interference pigments. These "colors" aren't easy to merge with even multidimensional color "wheels" (or matrices). Nonetheless, people typically interpret these pigments as colors.
A subtle factor is opaque vs. transparent color effects. These aren't mutually exclusive, but in "pure" form are distinct. Opaque colors may be mixed to form an intermediate color, but at lower saturation and value. More than not this is how people are taught to manipulate colors often in accordance with the basic color wheel.
Transparent colors may be mixed like opaques, with somewhat similar results. However, layering transparent colors potentially produces extended effects. While both opaque mixing and layered color are subtractive, layering can combine in several ways producing multiple "virtual" colors modified by filtering effects of layers.
Any color wheel, or multidimensional matrix, is unlikely to accommodate the numerous ways colors combine or mix, or non-color colors. Artists use color wheels or more complex structures to gain pragmatic info about the colors they're using and predict results of manipulations. In any case, most real-world paints, inks, etc., don't behave like pure colors. A color wheel is only valuable as a pragmatically useful tool.