It isn't surprising that chemical analysis is rarely used. Notwithstanding this problem, it has a number of advantages in practical situations. There are a few elements of dye identification by eye that can be learned from books, but not from photos in books because color reproduction is so imprecise. It's obvious that there is a danger that errors propagated from person to person can become accepted as truths simply by repetition. It's also a fact that there's so wide a variety of colors in both groups of dyes that educating our eye will require seeing thousands of examples under tutelage.
Knowledgable dealers can be very helpful, using their inventories as examples.
However, it would be far better to have many teachers and many more specimens than any small number of dealers is likely to be able to show us. The two best places to go for education are rug conventions that include Dealer Fairs, and previews of sales at major auction houses like Sotheby's, Christie's or Skinner's. These provide the opportunity to see and handle several hundred to several thousand rugs in a single place, with the opportunity to discuss them and ask questions of large numbers of people who have some expertise. Collectors, dealers, and auction house staff are all potential teachers, and are usually generous with their time and knowledge. There's no way to develop an educated eye without looking at lots of real rugs and getting taught by people who already have some experience.