Also largely mythology. There really is NO dual purpose bird, if by that you mean a bird that can perform into the top 90th percentile in egg production and also be in the top 90th percentile in time to market meat production.
The "idea" or dream of a dual purpose breed was developed into the agriculature, small farm culture of over a 100 years ago. Since then, Ag science has produced a true table meat bird that provides 99% of all chicken meat for table and resturant in the world.
Ag Science has also bred the spectacular commercial layers of white and egg table eggs. They're billion dollar babies, products of millions and millions of research dollars.
These old APA/ABA breeds serve no practical purpose in the modern world. They exist at all because folks with small holdings, niche breeders, and the exhibition hobby keep them from going extinct. These breeds date to a time and era before man could fly and we drove horses, and women washed clothes in buckets in the yard. Science moves forward and antiquities (which is what these birds are) are kept for enjoyment.