In Karate the black belts that are made with a silk top layer become frayed and after long use the black silk is almost all gone revealing what looks like a white belt underneath. Karateka relate this to the concept of 守破離 or Shu Ha Ri. Training is a circle where at black belt you understand the basics. As you train you become more of a master as the use of the belt causes it to wear away. At becomes white again you should come to know how little you really know and are like a beginner again with much to learn.
As a piper, don't get me started on kilts. I wear the Irish saffron kilt. I do think of the saffron kilt as the most beautiful of all and Itreat it as such.
The hakama should always be neatly folded and cared for no matter what shape it's in for dojo training. Public demos I think require a clean neat unfrayed hakama. Just my opinion.
The belt thing is a "myth added later". The belt system in Karate was adopted from Judo, before the war, by the Japanese, not the Okinawans (although it ended up leaking back). Judo added it from...swim classes, in schools, for children.
I wouldn't read too much meaning into it