I did several paintings using Gouache, using the Zorn palette–choosing Yellow Ochre, Ultramarine Blue, Alizarin Crimson, and black and white pigments.
The one advantage/disadvantage that I noticed was how much easier it was to select colors. If I wanted to make a color warmer I only had to choose the red or yellow. Making it cooler I had the blue. The disadvantage was the lack of control for making the color more intense. I was limited by the intensity of the colors in this palette. Intensity had to be controlled by other means such as edges and adjacent colors.
For this painting, I had to add a more intense yellow to show the intense light on the barn and some of the grasses near the barn.
The choice of a more intense yellow such as Cadmium yellow Light or Medium would be better but limiting in another way. Cadmium Yellow Light is a yellow with some blue in it and the medium has some red in it. Using the warm yellow with another warm color would not be a problem. Mixing the warm yellow with a cool color would make it less intense.
This cooler snow scene worked much better because the colors were less intense overall.
The pine trees presented the same problem with the yellow color. I again had to add a more intense yellow pigment to achieve the intensity that I wanted.
This last painting was the most successful of my experiments. Because the local colors of the subject matter were not intense to begin with, the limited palette was effective. It's great when everything works out.
In conclusion, I will not be adding black to my palette. With some of the new Quinacridone and Dioxazine pigments which are very intense and dark in value I have more options in mixing colors to achieve the values and intensities I'm looking for in my paintings.