Ours is white-stained cedar, has been the same way for over 20 years - we don't pressure wash it nearly as often as you say, actually. White stays cooler in the summer, in our experience.
If we want to change up the colors, it's much cheaper to paint the front door or the shutters than the whole house.
If there's a large section of your house that never gets any sun, you might have a mold problem, but that would show up on any light-colored house. We find a good shot with a regular hose or just regular dish soap or baking soda or vinegar takes care of it.