"But we must not think that in 2004 there is a single fish that is pure tomoin or yagozen. Each line has contributed to kohaku but none are created in a vacuum."
As usual JR you have added some wonderful words to the mix! Yes, definitely important not to take Koi bloodlines too literally,... more of a descriptive language. I generally say "Tomoin type", or "Sensuke type" when describing a Koi because it has characteristics that resemble those characteristics its anscestors were known for. In fact there is no such thing as "pure" Tomoin or Yagozen,... but rather certain characteristics a breeder produced and showed to the world regularly and consistently were "trademarked" or became the breeder's calling card.
Understanding the "characteristics" that came with the famous earlier bloodlines in Gosanke gives us a baseline in which to work from in our understanding of Koi traits and Koi development. These "types" of Koi generally develop consistently from fish to fish to fish, regardless of the breeder.
Best Wishes,
Brady Brandwod