I tentatively think that rain jackets would work better if they were more like coats of feathers.

Usually rain jackets are either (a) totally waterproof, in which case you sweat and it condenses on the inside of the jacket, or (b) "breathable", in which case they fairly quickly "wet out" and the sweat actually still condenses on the inside.

Feathers work partly like a "breathable" rain jacket, in that they're porous and hydrophobic on the outermost layer, but they're also anisotropic: rain jacket material is the same in all directions, while feathers work kinda like roof shingles: The water rolls off, but there's space for air to pass underneath the feathers. This is fine because rain mostly comes from above, and anyway I bet you can make fairly complicated labyrinths of air passageways such that even splashing water is very unlikely to make it through the jacket.