We have registered cattle also - so I understand your orientation to a breed.
Frankly, I wish there were pedigree registries for chickens....loads of people seem to not quite understand how it works...(Most if not all of the professional and/or experienced chicken breeders do, however.) Perhaps part of the high hurdle to jump would be that people would have to know not only which rooster produced that egg, but also which hen, and most chicken keepers group their hens in pens and don't know from which hen in the pen the egg was produced. Next hurdle is once in the incubator, even when the egg is marked, it is difficult once the chicks are out of the shell to tell who came from which empty eggshell.
on page 302 of Gail Damerow's book Story's Guide to keeping Chickens - she shows how to make a pedigree basket from hardware cloth - so that the egg(s) hatch inside the basket and the chicks can be identified then.
Another way to track a pedigree is allow the one rooster to run with hen(s) that have eggs that you can identify so you know for sure who is who. Glad that you thought of this...it would be nice to increase the awareness.... I guess too, with the ease at which chickens can be hatched and the short time frame -- it is an entirely different world than registered cattle.