A lot of feather colors are due to optical phenomena, not pigment. The extreme iridescence can show colors across the rainbow. Hair color development depends on color directly from pigments, so there is a smaller range of colors. A slight amount of iridescence in hair can develop, but is more restricted in color.
The optical structures in feathers are delicate and will wear down with age, so they tend to be a good measure of how healthy the individual that produced them is. Bird mating contests tend to do with female selection. The females are the ones that pick the most attractive mates. This has led to a feedback loop of more and more elaborate feather displays and resulted in the dramatics of Peafowl, or Humming Birds.
Mammals tend to use direct male to male competition for breeding selection. Its not all due to just the males, but it is a much higher component of the courtship. So the males still compete with each other, but it tends to be a more physical contest than a visual display.
The development of different animals skin covering plays a part as well. Feathers seem to be able to have complex structures arise easier. Hair tends to be much simpler in structure. Scales show more variety as well. Bare skin can range in color, amphibians show a large range in colors like birds do.
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