> there is nothing physically cyclic going on

If you plot the three primary colors with all possible combinations of only two of them, you can connect them all neatly using a circle, and distance on that circle does tell us something about how visually distinct colors are. It isn't much more profound than that.

One of the colors on the circle, magenta, has no corresponding pure wavelength, because in order to see magenta, your red and blue cones must be activated, but not the green cones -- you need two frequency peaks to do this. If we had four different types of cones, like many birds, there would be many more non-spectral fully saturated colors and you'd need something like a hypercube to represent them.