Because purple is a combination of wavelengths and the rainbow has only has the single wavelengths. It also missing “lighter” colors like pink and “darker” like brown
Purple is not a combination of wavelengths, it is a single one. And pink and brown are lighter/darker versions of other colors. Pink being light red, and brown being dark orange.
Depends on how you define purple. If violet is close enough to purple for you then that "purple" would be a single spectral color, a single or continuous set of wavelengths. If it's just a little more like magenta it would be a non-spectral color. A combo of red and blue light.
Plenty of non-spectral colors. Most things we see are non-spectral colors. Single pigments give off multiple wavelengths. Most things have combos of pigments on top of that. Emission spectra are multiple wavelengths.
Purple is often defined as the color we perceive when something reflects blue and red light, whereas violet is a specific region of the light spectrum between blue and ultraviolet.