Hue Rotate does have a Hue Scale slider, which will reduce the saturated colors in the clip to the visible spectrum. At 0 everything is reduced to red, at 0.25 it's reduced to red, orange and yellow, at 0.5 everything is reduced to red, orange, yellow, and green, at 1 nothing is reduced.
So, theoretically, with Hue Scale at 0, you could argue that the Hue Rotate param could be colored. With Hue Scale at 1 however, the color of the Hue Rotate param wouldn't make any sense at all. Should we then gradually fade out the 'coloredness' of the Hue Rotate param, the more you bring up Hue Scale? Sounds pretty hacky, a lot of work, ugly, and doesn't really add functionality.
An effect that can take a set dominant colors in a clip, and change them to a different set is my wet dream. When you take into account all Brady says, add on top that averaging color of a frame will result in grey, counting pixels will say its black, although our eyes will perceive it to be the most saturated color, and that a clip's colors can be completely different from frame to frame, I don't see this working without painstakingly adding metadata to each and everyone of your clips.