The original values are 3 dimensional and therefore best represented in a cube. If HSV is used, the hue is isolated to one dimension, which would represent the circumfrance of the color wheel you’re thinking of. The colors around the circular surface of your cylinder could be calculated from that, but you would be left with only one more display dimension and 2 more values: value (brightness/darkness) and saturation. You could only display one of them in the single empty dimension left in the cylinder.

Another way to explain why a cylinder is only good for representing two dimensions is simply that a circle asserts that length(x) == width(y) leaving only 2 values represented by a cylinder: (x,y) and z.