Because in this case we have a relatively simple ZKP for 3-coloring. However what you gain in the simplicity of the ZKP, you lose in the reduction to 3-colorin

Because in this case we have a relatively simple ZKP for 3-coloring. However what you gain in the simplicity of the ZKP, you lose in the reduction to 3-coloring. So nowadays people use ZKPs that work with more realistic computation representations, like arithmetic circuits