Where Did They Come From and Are They Really Worth Anything?
As previously mentioned, the reason the colors were chosen is because after Jigoro Kano awarded the first black belts to his senior students there was a significant gap in the skill level between the white and black belt. As an attempted resolution, he introduced the brown belt. There was yet another gap between the three so thus he added the green belt. Over the course of several years the gaps between the ranks continued to grow. More colored belts were added to the structure to balance the equation. It made sense to have the colors become darker with the progression of rank to black belt.
While karate performance ability might be the largest criteria, karate rank is a contract between an instructor and their student.