What are the advantages and disadvanatges of chromaticity diagrams?
The chromaticity diagram provides an abridged method to specify the hue and saturation of an unrelated stimulus or of metameric matches. That is really its only meaningful application. It has far more disadvantages such as having no representation of luminance, having no relationship to appearance, and having perceptually nonuniform spacing. I would recommend a review of the topic in Berns’ “Principles of Color Technology, 3rd Ed” for more details.