Blue is actually a big deal in the animal world. Apparently blue is a hard color combination to come by. Male bower birds are always on the lookout for blue objects when building their bowers.
The biggest problem is that humans only have a single pigment: Melanin, a dark brown pigment. You can get colors from yellow to red to brown to black, but no blues, greens or purples. (Well, not entirely true. There’s a few carotid pigments that are yellowish in color. Lipochrome is the one I can think of, but I don’t know any blue or green ones.)
Even eye color is done by melanin. The irises are actually a very light reddish brown (pink almost), but appear bluish due to Rayleigh scattering. Blue and gray eyes simply have less melanin-type pigment than brown eyes which is why they’re recessive.
Melanin is an excellent pigment because it protects against UV rays which is why brown and black tones are such popular colors in the animal kingdom – especially among mammals.
Maybe another reason is that mammals lost their ability to see much color during their early evolutionary history. Early mammals were nocturnal, and if you can shove more rods cells in your eye at the cost of some of the color seeing cones, you get better night vision. Having bright colorful coats doesn’t do mammals a lot of good. They make you easy to be seen by predators (birds and dinosaurs could see color), but they don’t impress the mammal babes.
Only old world monkeys gained the ability to see color, and that may explain why some old world monkeys have bright blue and red coloring in their faces. However, it appears these pigments never made it into the great apes.