Living organisms have developed a wide range of appearances from iridescent to matte textures. Interestingly, angular independent structural colors, where isotropy in the scattering structure is present, only produce coloration in the blue wavelength region of the visible spectrum. One might, therefore, wonder if such observation is a limitation of the architecture of the palette of materials available in nature. Here, by exploiting numerical modeling, we discuss the origin of isotropic structural colors without restriction to a specific light scattering regime. We show that high color purity and color saturation cannot be reached in isotropic short-range order structures for red hues. This conclusion holds even in the case of advanced scatterer morphologies, such as core-shell particles or inverse photonic glasses — explaining recent experimental findings reporting very poor performances of visual appearance for such systems.