It's really a case of birds, fish, reptiles, and various invertebrates vs mammals. Mammals are the odd ones out. The main reason is that bright colors are usually used for sexual selection or species identification. Most mammals lack full color vision and rely more heavily on scent and sound for sexual selection and species identification. So mammals lack a lot of the really bright coloration. Primates are the oddballs of the group that rely more on sight and less on smell.

Mammals do come in some pretty varied shapes though, not many equivalent groups contain species as diverse in body shape as bumblebee bats and blue whales. But in terms of decorative frilly bits, again, those are often about sight based signalling.