let me see if i can explain the version of the belt ranking system that seems to be pretty practical. To begin with a little about myself,,Ive been practicing Karate,, since the 60's and most of that time over sea's. This by far makes me an expert or master of my arts,,but ive been around and seen a lot,, so take what you want from this.
Master Kano Jigoro the found of Judo started using the belt system, to separate his begining, middle range and expert students for compitition. Before Dr Kano there was no belt system in Japan or Okinawa, in the martial arts.
He got this Idea (I understand) from watching swimming matches in japan,,that used a colored code for their swimmners,,the youngsters (beginners) middle students and advnaced students...Im not sure what colours they used..but Dr Kano decided on the White , Brown, Black,,
using the old Confucian, Zen, Tao ideas combined,,,, white (empty) brown a little more knowledge and Black being very knowledgable of the techniques.
This then was adopted by Funakoshi..and it began to be used in Okinawa after the war. As it was told to me.
On the practical side of not washing the belt,,back in those days after WWII no one had a awashing machine,,and and the Uniform (Gi) was very hard to wash,,,I remember back in the 60's training in Okinawa, (still washing machines were very uncommon) and the aroma of your opponent could win a sparring match
) ).. because they would only wash them once a week,,Wives had a hard enough time keeping up with washing family clothes that they had to wear,, the karate Gi,,was an honored thing,,but took a back seat to clothes that u had to wear in making a living. The belt was even harder to wash,,as it was much thicker and difficult to wash,,so they just did not wash it..and yes it would turn brown,,,,i have my original white belt,,and it is actually black in spots.. When My Sensei gave me the belt,,he told me,,that when the belt started turning black,,i would be on my way,,,well im 62,and it is turning black,,so i guess im on my way.
I remember many times training in Okinawa,,and visitors would come in to train with us, and would be wearing white belts,,that were kind of worn and raggedy,,out of respect to the Sensei at that Dojo they would wear a white belt,,but u knew they were far from being white belts.
Sometimes i wish it would go back to the days of
White, Brown , Black,,as it was when i started,, so many today lose the site of what the belt is about,,moreso,,they lose site of what the martial arts are about,,letting the rank cloud their ego..
You see so many with 10 stripes..stripes on both sides,,gold stripes , red stripes..standning around at tourneys, or siminars with their hands tucked in the belts.. watching???? oh well,,may be theve surpassed the reason to train.. sorry for the long post,,and hope u could get through it.