The article has a section on "why are clouds white?", but it doesn't really address the reason I thought that question should be covered.

It just says that clouds act like a collection of randomly-oriented prisms, such that whenever light of any wavelength comes into the cloud, it is dispersed from the cloud evenly in all directions.

This would explain why a cloud was white if even white light was coming into the cloud. But the rest of the article establishes that the light coming into the cloud is predominantly blue and purple. Why isn't that also true of the light leaving the cloud?

Well, no; what's coming into the cloud is sunlight, filtered through the atmosphere. It scatters that light and so it has that color. The same like a heap of powdered salt in the palm of your hand, held up to the sun.

Clouds illuminated by the setting sun aren't white.