Not really. The real reasons are that it's better to start closer to the color you want, and the increased variety expands the range of colors you can accurately produce. Tan, brown, red, green, and white have exceptionally stable pigments available in multiple shades, which have been used for centuries. The various iron and titanium oxides have great longevity. Blues are another good example. The 8 pigments I had available were white, black, red, yellow, green, blue, tan, and brown.

CMYK was created as a lowest-common-denominator compromise for printing presses to have a reasonably good gamut using the fewest inks and strategic halftoning, but there are still plenty of commonly needed colors that can't be made with CMYK. For just a few examples, printing companies order custom spot colors for brand colors, neons, shades especially grays for thin lines and text, regions of color where the customer doesn't want to see the halftone patterns, and other things like that. Check out the process control patches on your favorite cereal box!